Important Things While Choosing Online Math Tutor

Important Things While Choosing Online Math Tutor 0SHARESShare Math is a subject that involves lots of mental applications and logic. This has made most of the students shudder at the subject. They are stricken with panic to take up Math courses. Getting extra help to come out of their difficult phases in Math doing is a very common one. While doing so, they need to be careful in their choice of online math tutor. Things to notice while choosing a Online Math Tutor Credentials: Check whether the tutor is qualified to handle the area you want to get help. If you are disturbed with Algebra and wish to get clarifications in its equations and expressions, you should check up that the online tutor you hire has expertise in the field and is able to handle any challenge with efficiency. Experience: Experience plays a major role in buying a Math tutor online as he would have dealt with many students and tasks and would be able to help you in any difficulty with confidence. Exposure: The knowledge of the tutor should be up to date that he is able to suggest resources for your further study and research. The tutor’s exposure to the field is very important from this angle. Student friendly: Patience and versatile teaching methods play a major role in a tutor’s success in Math. Working with the student on a white board expects great patience and remarkable insights about the subject. A good Math tutor should be able to anticipate the possible errors of the student beforehand. Authenticity of the tutoring site you join: Many tutoring sites online have no proper record of establishment and success. So, ensure their existence in the tutoring market to avail their services in a safe manner. Math assignment help from Tutor Pace have all the above mentioned features and you would find yourself safe in their hands. Our Math homework help is available with solutions for even the most daunting tasks in all branches of Math. [starbox id=admin]

Learning Violin

Learning Violin Top Tips for Learning How to Play the Violin ChaptersHow Can You Learn How to Play Violin on Your Own?Can You Take Violin Lessons without Knowing Music Theory?How Can You Learn How to Play the Violin Online?How Can You Learn to Play the Electric Violin?How Can You Learn Violin Vibrato?The violin is often thought of as one of the harder orchestra instruments to learn and is seen as inaccessible to many.Of course, this becomes less true by the day. In recent years, new ways of learning have helped bring the violin (or fiddle) to almost everybody. Playing violin is for everyone, after all.There are violin lessons near me in music schools for those wanting to learn more about music, improvisation, positioning their left hand, reading sheet music and notes, or just improve their playing.Additionally, you can learn on the internet, with manuals, guides, and books, and private lessons. Find out which is the best way for you to learn the violin.How Can You Learn Violin Vibrato?Once you’re getting good at the violin, you’ll have to learn some of the intermediate and advanced playing techniques. Vibrato is one of the most common ones.Vibrato is the act of varying the pitch around a given frequency.This technique gives an undulating effect.  The vibrato can help add expression to a piece. You therefore need to know the right time and place to use it.  To perform vibrato on the violin, you need to be good at positioning your fingers on the neck.Generally speaking, vibrato isn’t taught until the second or third year of tuition.  To learn vibrato, you need to do a back-and-forth motion with your left arm. The finger being used to press down on the string will pivot back and forth from its initial position.  You’ll have to practise this a lot in order to get it right. However, after a while, this action will become second nature to you.  If you’re a beginner, be patient! You don’t want to walk before you can run and teach yourself to do it wrong.Don't forget that if you feel like the violin isn't for you, yo u can get singing, clarinet, or piano lessons, etc. from the many private tutors on Superprof.

Circumference Equation

Circumference Equation A circle is set of all the points that are in the same plane and equidistant from a central point. The radius of a circle is a line segment that joins center of the circle and any point on the circle. The circumference equation involves calculation of circles circumference or perimeter. Circumference is the distance or path around the circle. The circumference equation is pie multiplied by diameter. The formula for circumference of a circle is 2r. The formula for the length of arc with central angle is x (/180) x r. Circumference equation is a very useful tool. Example 1: A Gardner has to plant a bush round the circular park. The distance from the center of the park to the edge of the park is 50 m. Find out the length of the bush. Solution 1: We have given, radius r = 50 m. Circumference of a circle = 2 r We get, = 2 x 50 = 2 x 3.14 x 50 = 314 m. The Length of the bush will be 314 m. Example 2: In the below mentioned figure, find the circumference of the circle. Solution 2: Given, Radius of circle = 70 cm In this question we have to find the circumference of circle. We Know that, Circumference of circle = 2 x pie x r Here pie = 22/7 or 3.14 and r = 70 cm Therefore, Circumference of circle = 2 x 22/7 x 70 = 440 cm.

How to Sing in a Deeper Voice

How to Sing in a Deeper Voice Increase your Vocal Range to  Sing in a Low Voice Chapters4 Things to Avoid if You Want to Work on the Low Notes5 Steps You Should Take to Sing with a Low VoiceSingers for Working on Lower NotesThe Best Songs for Singing with a Low VoiceWe should say right at the start that there’s no easy way to sing in a low voice!  Anyone who’s promising you (especially music schools and teachers) that singing in a low voice is something you can do easily is a liar. You need to put a lot of work into your voice with your singing teacher if you want to improve, perfect, and even master your singing voice and vocal technique.The current trend for singers with a low voice to gravitate towards musical styles like blues, soul, or jazz.  As we already know, even with all the talent in the world, a nice timbre, and fantastic stage presence, it can still be difficult to reach certain octaves and notes. Especially for beginners!Regardless of how they sound, there are good singers and there are bad singers.  A good singer is one who is fully aware of w hat singing requires both in terms of their body and their attitude.  These are the kinds of singers who are happy to learn new vocal techniques and listen to advice from their very first lesson until they’re about to step on stage in front of thousands of spectators.In this article, we've put together singing tips to help you learn how to sing the lower octaves. TraceySinging Teacher 4.92 (13) £25/h1st lesson free!Discover all our tutors PortiaSinging Teacher 4.91 (11) £35/h1st lesson free!Discover all our tutors NicolaSinging Teacher 5.00 (11) £40/h1st lesson free!Discover all our tutors JazzSinging Teacher 5.00 (6) £40/h1st lesson free!Discover all our tutors PerrineSinging Teacher 5.00 (3) £50/h1st lesson free!Discover all our tutors TiemSinging Teacher £40/h1st lesson free!Discover all our tutors TomSinging Teacher £25/h1st lesson free!Discover all our tutors MiriamSinging Teacher 5.00 (4) £35/h1st lesson free!Discover all our tutors4 Things to Avoid if You Want to Work on the Low Notes1. Trying to Change Your Vocal CordsWithout surgery, it’s impossible to change the length of a person’s vocal cords. This is what will generally define a person’s tessitura.There are plenty of good exercises for hitting lower notes. (Source: pixabay.com)For example, some modern singers, both amateur and professional, will find it easier to sing in high notes than low notes and vice-versa.It’s much easier to work with your biology than to attempt to go against it by changing your vocal range. That said, vocal training can help expand your range.2. Forcing Your VoiceIn almost every case, forcing your voice is a really bad idea. Whether you’re trying to get an entire classroom to be quiet, make yourself heard in a debate, or screaming at your favourite artist as they perform, we tend to occasionally put our voice through the grinder.Whether you’re a singer in a band, a choir, or a solo artist, forcing your voice could lead to you losing it for at le ast a few days.Looking for singing lessons manchester?3. Not Resting Your VoiceIn our daily life, overworking can have a massively negative effect on us. The same can happen to our voice if you don’t treat it with respect.It’s important that a singer respects their voice by giving it the appropriate amount of rest after working it so hard during a song.Singing song after song without any rest at all can be really bad for your voice and can result in the subsequent performances being worse than if you’d otherwise rested. Make sure you always rest your voice after each of your voice lessons.4. Lowering Your Head to Sing Low NotesWhile this is a general human reaction, it’s something you should avoid at all costs because it won’t make your life any easier. Lowering your head will not make it easier to produce low notes!You should also learn how to master vibrato, one of the most important singing techniques for opera singers.5 Steps You Should Take to Sing with a Low VoiceSin ging with a low voice is not walk in the park. It takes a lot of time, dedication, and, in some cases, money. It requires that you work on your posture, breathing, and vocal exercises in order to get there.1. Unlock Your FaceIn order to sing better, you’ll need to relax your face.While this is the tensest part of a lot of people’s bodies, unlocking your face can help you hit both lower and higher notes.Don't forget that it's your breath that can give your voice most of its power. (Source:  Thibault Trillet)There are several techniques that can be used to do this. There are several bad habits you should also avoid:Loosen up your jaw. This area exerts the largest amount of force on your face. To do this, unclench your teeth and let your jaw lightly fall. This should relieve tension in your face.Relax your eyes and your forehead. Focus on your eyebrows and eyelids. The goal is to relax our facial features over time.Work on your tongue and your mouth. These are essential parts when it comes to singing. By vibrating your lips and proudly showing off your teeth, you can improve your elocution and your production of low notes. Finally, place your tongue flat with the tip of your tongue on your lower set of teeth.2. VocaliseThis is the a classic method. Making a few low “oohs” are a good way to broaden your vocal range without needing to use technology like a vocoder.While some students hate this exercise, it’s a favourite amongst most singing teachers and voice coaches and can:Make the vocal cords more flexibleImprove your voiceHelp students sing every note in their rangeImprove your vocal rangeIt should be noted that carrying out a few vocalisations while being accompanied by a piano is a great way to work on your vocal range.There are other exercises to help you sing in a low voice like using your chest voice for notes you can already sing with your head voice without changing your tessitura.3. Use Diaphragmatic BreathingTo add more to your voice, assert your presence on stage, or just make your voice more pleasing, you have to work on diaphragmatic breathing.To do this, you need to:Push out your stomach as you breathe in.Progressively bring your stomach back in as you breathe out.Lightly push on the obliques around the pubis.Make your diaphragm rest low as long as you can.Bring your stomach back in as slowly as possibleExpand your rib cage as much as you can.4. Work on Moving Air Around Your Body to Improve Your BreathJust like in martial arts and tai chi, breath plays an important part in singing and can define the quality of your voice and a singer’s performance.The air that becomes your breath needs to come from the bottom of your stomach and needs to be controlled completely. Being aware of your breathing is the first step towards improving your singing.5. Take Singing Classes with a Singing TutorWe’re not going to lie, while there are plenty of resources for learning how to sing, online singing lessons, and YouTube videos on the subject, none of these can really replace a private vocal coach giving you feedback from the comfort of your own home.While you can teach yourself to sing, you’ll get better results with a private voice teacher who can tailor their lessons to you and work on the vocal techniques that you need to improve your abilities as a singer.If you feel this is the option for you, then you should head straight over to Superprof’s main page and start looking for singing tutors that live near you.This is arguably one of the most cost-effective methods for learning how to sing since every hour is spent working exactly on what you need to work on. Your tutor will also choose the best singing exercises for you, help you work on your breath control, improve your vocal health, and show you the vocal warm up exercises you should be doing before every voice training session.If you’re not sure, you can look through the different tutors available, see how many years of experience they have, t he qualifications they’ve earned, their teaching approach.  Additionally, you can always have a look at the opinions of their former and current students to see whether the tutor is right for you.Find singing lessons London or singing lessons online.Singers for Working on Lower NotesWhile vocal ranges can cover bass, baritone, tenor, alto, mezzo-soprano, and soprano, there’s something really special about hearing the lower ranges.Even if you have an instrument to back you up, you should take special care of your voice. (Source:  Agnes Talalaev)A search for “deepest voice in the world” will probably put you off trying to lower your vocal range. However, there are plenty of accessible artists who also sing in lower range.Male Artists with Low VoicesNick CaveLeonard CohenBarry WhiteTom WaitsJim MorrisonHowlin’ WolfWillie DixonBB KingBruce SpringsteenElvis PresleyFemale Singers with Low VoicesTina TurnerWhitney HoustonTracy ChapmanLauryn HillAmy WinehouseAdeleCherChristina Agu ileraToni BraxtonIndilaIf you want to get the most out of your voice, you should look at hiring a private singing tutor. (Source: Thibault Trillet)The Best Songs for Singing with a Low VoiceFiver Finger Death Punch â€" House of the Rising Sun (Cover)Bill Withers â€" Ain’t No SunshineConway Twitty â€" Slow HandDarius Rucker â€" Don’t Think I Don’t Think About ItJosh Turner â€" Your ManToby Keith â€" I Love This BarWar â€" Low RiderLips of an Angel â€" HinderThe Calling â€" Wherever You Will GoThe Big Bopper â€" Chantilly LaceJohnny Cash â€" Hurt

Dealing with FOMO as an Introvert - Introvert Whisperer

Introvert Whisperer / Dealing with FOMO as an Introvert - Introvert Whisperer Dealing with FOMO as an Introvert Kayla Matthews July 19, 2019 Dealing with Fear One response Go to top We hear about it all the time â€" FOMO or the fear of missing out. Marketing campaigns have been utilizing this fear in their ad campaigns for years, reminding you of the things that youll be missing out on to encourage you to buy products or invest in services or experiences. The problem with these marketing tricks is that they dont appeal to everyone. As an introvert, you have to balance your fear of missing out with your desire to stay home and avoid social interaction. How can you deal with FOMO as an introvert? Stop the Social Media Binge If youre suffering from FOMO, social media is the worst place you can go to. Social media doesnt just give you a place to showcase all of your adventures â€" it actually generates that fear of missing out, because you get to see what everyone else is up to. They might be doing things that youd enjoy, but you werent invited so it triggers that FOMO feeling. A study published in the Journal of Social and Clinical Psychology found that restricting social media use to 10 minutes per day per platform improved mental health and reduced symptoms of depression as well as feelings of loneliness. If you cant reconcile your FOMO with your introverted tendencies, try shutting off your social media or at least reducing your use. Realize You Arent Missing Out Do you know what they say about FOMO? Jealousy is all the fun you think they had. You only see the best highlights of whatever everyone else is doing, especially on social media, so you build up this amazing event in your head that you feel bad for missing out â€" whether its true or not. It gets even worse as an introvert â€" either you decided not to go, or you werent invited because your friends know youll probably say no anyway. Either way, we get it â€" it sucks. Itll take time but if you understand that you arent actually missing out, FOMO becomes easier to handle. Take Time To Recharge Socializing as an introvert is one of the most exhausting experiences of your life. Thats because introverts recharge when theyre alone, and being in social settings drains their batteries. If you do decide to go out, dont spread yourself too thin. Make sure youre giving yourself time to recharge between events. It could be as simple as staying home to take a bubble bath and watch Netflix or as complex as spending the afternoon at a spa getting pampered. Whatever you need to recharge, make sure youre giving yourself enough time to keep your batteries topped off. FOMO Sucks â€" Dont Let It Bother You We get it â€" FOMO sucks. You dont ever want to feel like youre missing out, but it can be difficult to keep up with an extroverts busy social schedule when all you want to do is stay home, eat junk food, and sleep. Stop worrying about missing out and start taking care of yourself. Worry about making your own memories and enjoying your experiences, rather than trying to live the perfect Instagram life. FOMO can only bother you if you let it. Take care of yourself first. Go to top Bottom-line â€" I want to help you accelerate your career â€" to achieve what you want by connecting you with your Free Instant Access to my 4 Building Blocks to Relationships eBookâ€" the backbone to your Networking success and fantastic work relationships.   Grab yours by visiting here right now! Brought to you by Dorothy Tannahill-Moran â€" dedicated to unleashing your professional potential. Introvert Whisperer

Where Can I Buy Sewing Patterns

Where Can I Buy Sewing Patterns The Best Places to Buy Patterns for Sewing ChaptersFind a Sewing Pattern at HobbycraftPatterns at AbakhanFinding Patterns in Your Local Sewing ShopShopping for Patterns OnlineIf you know how to sew, you have an advantage over everyone who is limited to buying clothing in a shop: you can make any article of clothing you wish, in any colour or type of fabric you wish.Unfortunately, clothing oneself is not as easy as draping a length of cloth around oneself, at least in most countries.Naturally, you may opt to wear elegant saris or a gracious kimono but you would still need undergarments and they must be sewn.Today, sewing your own clothes is more of a novelty than a necessity.Still, judging by all of the activity in fabric and sewing supply stores, it appears that sewing is enjoying a resurgence.Perhaps you too have decided to dust off your sewing machine and put it to good use.Maybe you feel inspired by the gorgeous fabric you found that would look stunning as a summer dress or a wrap skirt. Or maybe you could make the most of it by making a wrap dress… Although they are both a type of wrap dress, you cannot sew a kimono from a wrap dress pattern! Image by Sasin Tipchai from PixabayTake amazing sewing courses here.Ah, here comes the indecision: what to make of those three metres of fabric you fell in love with? And how to make that article of clothing, once you settle on what you want to make?The answer to both of those questions is one and the same: a pattern.In this article, your Superprof prowls around the best fabric and notions stores to help you find the best places to buy dressmaking patterns and patterns for other articles you might consider sewing, such as doll clothes and purses.Did you know that purse patterns were a thing?knitting and crochet.Naturally, they have a whole line of sewing supplies, including patterns.How would you like to make a tunic top with an asymmetric hemline? Or maybe you’d like to make yourself a smart cape for those evenings you go to the theatre…Hobbycraft offers so much more than just a handf ul of patterns and definitely more than clothes patterns; they have patterns for doll clothes, costume patterns for fancy dress â€" are you going to a fancy dress party for New Years?So far, we’ve only mentioned women’s clothing but did you know that Hobbycraft has patterns for men’s clothing as well?You can find trouser, vests and pajama patterns and more than one shirt pattern suitable for men, you can also find many patterns for loungewear for both men and women.They stock lots of patterns for children’s clothing, too. Everything from fun rompers for active play to sleepwear to snuggle down in.Offhand, it sounds a bit overwhelming, the selection they keep on hand but you needn’t worry about being subsumed by sewing patterns; to make your selection, you may simply look through their catalogues for a style that suits you. The shop attendant will then go find the pattern for you.The only way that process could be made more effortless is by learning how to make your own pat terns! You may delight in a Simplicity pattern to make these vintage dresses! Image by ????????? ???? from PixabayPatterns at AbakhanWhere Hobbycraft has something for everyone dabbling in virtually any hobby from sewing to painting, Abakhan deals almost exclusively in fabrics and the needle arts.And, much like the other chain hobby craft store already mentioned, you can find an Abakhan in just about every UK city.Ok, that is a bit of an exaggeration.Still, if you’re wondering where in Altrincham, Bolton or Preston you could go to look at a selection of patterns, you need only look for the bright green Abakhan banner.Once inside the store, you will be greeted by friendly, helpful clerks who will do their utmost to help you find the pattern you are looking for.Even better: if you are brand-loyal, you will surely find what you are hunting because they have their patterns catalogued by name:Burda StyleButterickDMCHayfieldSimplicityKwik SewMcCallsVogue PatternsSimple SewTilly and the ButtonsA s though their wide selection of brands wasn’t generous enough, they also have doll clothes patterns, patterns for pet wear, bag patterns and patterns for home decoration accessories like pillows and seasonal item.And, if you enjoy the casual comfort of medical scrubs, they have patterns for those, too.Should there not be such a fabulous store in your city, you may shop their website for the pattern you crave, or even just to get ideas of what you could make with that fabric you just bought.By the way, did you know you could also learn how to make your own dress pattern?Finding Patterns in Your Local Sewing ShopRight after shopping online for everything from groceries to digital goods like music and films, chain stores are the go-to choice for most shoppers.And why not? They are convenient, competitively priced and they always seem to have what you need when you need it.While they are a boon for shoppers, such ventures usually make things more difficult for the independent retaile r who often struggles with the same issues that plague those big box stores without the benefit of a corporation’s bank book to back them.And, with taxation and regulation making it ever harder for the independent shops to keep the doors open â€" let alone to make a profit, supporting our local businesses could be seen as doing one’s civic duty.Besides, your local sewing supplies store clerks most likely have a wealth of experience and advice you could benefit from, such as which fabrics would flow best for that A-line dress you wanted to make or any hacks for sewing a knit dress.In fact, there is a good chance that you will be offered sewing tutorials; you may even get some instruction on pattern making!All across the UK, there are delightful shops, often tucked away from the main thoroughfares, that are just brilliant in their resources and knowledge about sewing. Here, we’ve compiled some of the best.Independent Sewing Shops Across the UKCityShop NamePhoneBristolFlo-Jo0117 904 1498BirminghamGuthrie Ghani0121 449 8419CardiffTrixieLixie0292 034 4464LeedsFabrics for All0113 279 5007LondonStag Bow 0208 291 4992NottinghamColes 0115 988 1550PlymouthFunky Poppy0777 675 7300YorkGillies' Fabrics0190 462 6244You may even find that those shop owners are passionate about the needle arts and may impart to you pattern-making basics of fashion design. If you are looking for beginner sewing projects, you might look for doll patterns Image by Hans Braxmeier from PixabayShopping for Patterns OnlineYou might imagine that, if we were surly about chain stores taking business away from the independent stores, we must be downright hostile about online shopping sites… right?Quite the contrary, as it turns out!Let’s go back to our opening scenario: you just bought three metres of dazzling fabric and you are not quite sure what you want to make out of it.Earlier, we implied that you could look at the sketches on pattern envelopes, sort of flip through them â€" like Sheldon (The Big Bang) flips through comic books, to see if any design catches your eye.The next best step would be to thumb through a catalogue.Major pattern makers each have their own collections of patterns, so you might first look at a catalogue of Simplicity patterns, and then a collection of Butterick patterns…You may even be interested in looking at vintage sewing pat terns from those two major brands; after all, they have been around for over 150 years.The easiest way to decide on a pattern is to look online.If you don’t feel like spending hours in a brightly-lit shop, thumbing through sewing books and you don’t have an eclectic home-grown sewing shop nearby, your best bet to see a wide selection of clothing patterns is online.The two chain retailers we mentioned both have websites with an entire page dedicated to the patterns they have in stock.Amazon, the giant of online sales, also has a selection of dress patterns available.However, their selection is fairly limited; for instance, they don’t have much in the way of clothing for men and only a few patterns for children’s clothes.Here, we have to mention the revolution in clothes patterns: digitising them.Many designers are scanning their patterns in or drawing them outright with computer drawing software, and then making their patterns available, either as a PDF download or paper patt erns.The advantage over the PDF files is that they are a bit less expensive than the other ones.One of the greatest benefits to sites such as Closet Case Patterns and others like it is that the sizing is a bit more generous than, say, a Simplicity sewing pattern.Much as we enjoy your company, isn’t it time you go look at websites with clothes patterns?Oh, and before you make your first cut in that gorgeous material of yours, come back so we can show you how to adjust your patterns for size, length and the type of material you’re working with.Yes, that is an important factor when choosing your pattern!

GMAT Quant Strategies Summing an Arithmetic Sequence

GMAT Quant Strategies Summing an Arithmetic Sequence GMAT MBA Admissions Blog One of the more difficult GMAT problem types deals with summing an arithmetic sequence. Problem 157 in the 12th edition Official Guide is an example: 157. For any positive integer n, the sum of the first n positive integers equals (n(n + 1))/2. What is the sum of all the even integers between 99 and 301? (A) 10,100 (B) 20,200 (C) 22,650 (D) 40,200 (E) 45,150 In this problem the GMAT provides us with an equation, and we can use that equation along with a bit of algebra to solve the problem. However, this might not always be the case, and no doubt in the future the test writers will introduce problems without helpful hints - indeed there are a couple in the 12th and 13th editions of the OG. Consequently, students should know how to do this type of problem in general. First a definition: Arithmetic sequencesare ordered lists of numbers (on the GMAT these numbers are most likely integers) where the difference between adjacent numbers is constant. The most common example on the GMAT are lists of consecutive integers. For example: {1, 2, 3, 4, 5, 6}, or, in general, any list of the form {x, x + 1, x + 2, x + 3...} Arithmetic sequences are similar, but the difference between the terms can be anything. For example: {3, 7, 10, 13, 16}, {1/2, 5/2, 9/2, 13/2}, {2, 4, 6, 8, 10, 12, 14}, or, in general {x, x+ d, x + 2d, x+ 3d...} Everything we need to know about an arithmetic sequence can be summed up in three pieces of information: 1. The first (or last) term 2. The difference between the terms 3. The number of terms For the most part, the first two pieces of information are explicitly or implicitly stated. If we are summing even integers, the difference is two and the first and last terms must both be even regardless of the range stated in the problem. The third piece of information is something we generally have to derive for ourselves. I'm going to use a simple example to explain how to do this. How many integers are there between 7 and 15, inclusive? Intuitively, it seems like we should find the difference between the two numbers, 15 - 7 = 8, and that will be the number of terms. If we take the brute force approach of actually listing the integers we find that the intuitive approach is off by 1: {7, 8, 9, 10, 11, 12, 13, 14, 15}. If you count the integers, you'll find that there are nine of them in the list. It might seem like we should just take the brute force approach every time we need to solve this sort of problem, but for larger sets this would be impractical. So, why is the intuitive approach incorrect? It pretty simple - by subtracting the 7, we don't include it in the set, and the count is off by one. To compensate for this, we add one to the difference. If x is less than y, the number of integers between xand y, inclusiveis y- x + 1 We have to modify this formula if we want to use it count an arithmetic sequence where the difference between terms is greater than 1. If d is the difference between the terms in the sequence, and xis less than y, then the number of terms in the sequence is (y- x)/d + 1 We have to be a bit careful applying this formula. If we're asked to find the number of multiples of 3 between 2 and 34, our first term is not 2, it's 3, and our last term isn't 34, it's 33 - this is because we're only counting multiples of 3. So, now that we know how to count the number of terms we can move on to finding the sum of the terms. First we need a couple of definitions 1. The averageor arithmetic meanof a set of numbers is The sum of the terms/The number of terms For example, the average of the first 5 positive even integers (2, 4, 6, 8, and 10) is (2 + 4 + 6 + 8 + 10)/5 = 30/5 = 6 2. The medianof a set of ordered numbers is the middle term of the set or the average of the two middle terms. That is, if an ordered set has 5 numbers, the 3rd term will be the median; if an ordered set has 6 numbers, the average of the 3rd and 4th terms will be the median. Two examples: To find the median of the set {8, 17, 7, 13, 4}, we order the terms of the set from least to greatest (or vice versa) and find the middle term. The middle term of the set {4, 7, 8, 13, 17} is 8. So the median of the set is 8. To find the median of the set {8, 17, 7, 13, 4, 31} we follow the same procedure, but now we take the average of the two middle terms. The average of the two middle terms of the set {4, 7, 8, 13, 17, 31} are 8 and 13. So the median of the set is (8 + 13)/2 = 10.5 Arithmetic sequences of numbers have the nifty property that the median and mean of the set are the same number. Mean of an arithmetic sequence = Median of an arithmetic sequence Furthermore the mean of an arithmetic sequence is just the average of the first and last term, and since the median is equal to the mean, the median is also the average of the first and last term. If this seems mysterious, remember that there is a geometric interpretation of the mean. The mean of two numbers on the number line is the midpoint, e.g. the mean of 1 and 7 is 4, because the distance from 1 to 4 is equal to the distance betwen 4 and 7. In an arithmetic sequence the midpoint between the first and last term is exactly the median. Now let's derive the formula for the sum of an arithmetic sequence. Recall that Mean = Sum of terms/Number of terms Therefore (Mean)(Number of terms) = Sum of terms So, if xis the first term of an arithmetic sequence,yis the last term, and d is the difference, the sum of the sequence is [(x+ y)/2][((y - x/)d) + 1] = Sum of terms Now let's return to problem 157 from the 12th OG: 157. For any positive integer n, the sum of the first n positive integers equals (n(n + 1))/2. What is the sum of all the even integers between 99 and 301? (A) 10,100 (B) 20,200 (C) 22,650 (D) 40,200 (E) 45,150 Because we are only concerned with the even integers, the first term of the sequence is 100 and the last term of the sequence is 300. The mean of the sequence is (100 + 300)/2 = 400/2 = 200 The number of terms in the sequence is ((300 - 100)/2) + 1 = (200/2) + 1 = 100 + 1 = 101 Thus, the sum of the sequence is (101)(200) = 20,200 The explanation is the OG is much more convoluted, with unnecessarily obscure notation. The method presented here is clean and quick. Try it for yourself. 1. Find the sum of the first 100 positive integers 2. Find the sum of all the multiples of 3 between 1 and 100 3. Find the sum of the multiples of 7 between 47 and 624 4. The sum of a set of 50 consecutive positive odd numbers is 172. Find the fist and last term of the sequence I hope you enjoyed this post. I will post answers to the questions with explanations in a subsequent post. Please visit our GMAT Tutoring page to learn more about MyGuru's approach to test prep. About the Author John E. is a Senior MyGuru GMAT tutor in Chicago. He also tutors the GRE, SAT, ACT, and almost anything math related. He holds a B.S. in Mathematics and English from Indiana University, and a M.S. in Mathematics from UIC. He's scored in the 99th percentile on all of the above standardized tests, and has worked for MyGuru and other companies to develop proprietary test prep questions and explanations of difficult quantitative concepts to help students improve their GMAT scores. He's currently working with MyGuru to develop proprietary test prep material focused on the most difficult GMAT question types. Are you interested in more GMAT explanations and practice problems that are similiar to the above? hbspt.cta._relativeUrls=true;hbspt.cta.load(215486, 'c962711f-eb4d-4fa9-9c75-db61122354d0', {});

The College Search Checklist What Your Teen Should Consider When Evaluating Colleges

The College Search Checklist What Your Teen Should Consider When Evaluating Colleges Choosing a college is one of the most important decisions of your teens life. While exciting, the process of identifying schools and narrowing the list can be overwhelming to many students. CEO and Co-Founder, Eileen Huntington of Huntington Learning Center says the best way for parents to help is by reminding their teens that there are several essential components to evaluating colleges. Too often, teens get their hearts set on one or two things and ignore everything else, she says. Its important to focus on what matters most and not overlook the factors that really make the college experience. She offers this list of key considerations for teens and parents to keep on hand when embarking on the college search: Fields of study Whether teens are certain about a college major or still deciding, its a good idea to ensure any college on their short list has a range of enticing options. Keep in mind that changing majors early in college is common, so parents should caution their teens to not paint themselves into a corner. An engineering college is a great option if theres no chance your teen will end up deciding to switch gears to his or her backup plan, pre-medicine. Size Many teens know right away what theyre looking for as far as student population, but if your teen isnt sure yet, talk about it. Larger universities offer more academic options and the chance to engage in opportunities like undergraduate research. Many also have graduate programs too, if your teen is thinking about taking that path. Smaller schools will have a lower faculty-student ratio and a more intimate classroom and campus feel. There are advantages and disadvantages of both, and its important that teens think this through. Proximity to home Teens who have their hearts set on moving far away for college need to understand the logistics involved in doing so. Parents and teens should discuss things like how often their teens will be able to visit home (because of costs and time involved) and the value that their teens place on having a support system in their new area. Cost and financial aid This is an important consideration, but its hard to make an informed decision by looking at a colleges tuition schedule on their website. A true college price tag will take financial aid assistance and scholarships into account, so while it might be tempting to rule out colleges that have a sticker price that is out of reach, you and your teen should do a little digging. Talk with each colleges financial aid office to learn more about typical financial aid packages, the best approach to applying for scholarships, and more. Campus life Most students go to college to grow both academically and personally, and campus life plays a big part in that transformation. Teens should get a feel for what life is like at a college, either by visiting in person or by talking with current and former students and scouring the colleges websites. Does the college offer the kinds of social and student life opportunities they are seeking? Is there a lot going on outside of the classroom (e.g. athletic events and other fun activities)? What is dorm life like and how many students live on campus as freshmen? Without a doubt, choosing a college is a major decision, but the process can be made simpler when teens take a systematic approach to comparing and contrasting different schools, Huntington says. Our advice at Huntington is to let teens take the reins on this process, as they are the ones who must feel confident in the decision. Offer them a framework for assessing each college, encourage them to take advantage of the knowledge and expertise of their high school guidance counselor, and weigh in when you need to. With this approach, teens are sure to make a smart decision that they will be happy with in the long run. About Huntington Huntington is the tutoring and test prep leader.Its certified tutors provide individualized instruction in reading, phonics, writing, study skills, elementary and middle school math, Algebra through Calculus, Chemistry, and other sciences. It preps for the SAT and ACT, as well as state and standardized exams. Huntington programs develop the skills, confidence, and motivation to help students succeed and meet the needs of Common Core State Standards. Founded in 1977, Huntingtons mission is to give every student the best education possible. Learn how Huntington can help atwww.huntingtonhelps.com. For franchise opportunities please visitwww.huntingtonfranchise.com. 2018 Huntington Mark, LLC. Huntington Learning Center, the three-leaf logo, and 1 800 CAN LEARN are registered trademarks of Huntington Mark, LLC. Each franchised Huntington Learning Center is operated under a franchise agreement with Huntington Learning Centers, Inc.