How to Find the nth Term of an Increasing Linear Sequence.

Updated on November 26, 2016

Nth Term Of Increasing Sequences Video

The nth term of a number sequence is a formula that gives you the values in the numbers sequence from the position number (some people call it the position to term rule).

Example 1

Find the nth term of this sequence.

5 8 11 14 17

First of all write the position numbers 1 to 5 above the top of the numbers in the sequence (call these numbers at the top n). Make sure you leave a gap.

n 1 2 3 4 5 (1st row)

(2nd row)

5 8 11 14 17 (3rd row)

Next, work out the difference between the terms in the sequence (also known as the term to term rule). It is quite clear that you are adding on 3 each time. This tells us that the nth term has something to do with the 3 times table. Therefore, you multiply all the numbers at the top by 3 (just write your multiples of 3). Do this in the space you have left (the 2nd row).

n 1 2 3 4 5 (1st row)

3n 3 6 9 12 15 (2nd row)

5 8 11 14 17 (3rd row)

Now, you can see that if you add on 2 to all the numbers on the second row you get the number in the sequence on the 3rd row.

So our rule is to times the numbers on the 1st row by 3 and add on 2.

Therefore our nth term = 3n + 2

Example 2

Find the nth term of this number sequence.

2 8 14 20 26

Again write the numbers 1 to 5 above the numbers in the sequence, and leave a spare line again.

n 1 2 3 4 5 (1st row)

(2nd row)

2 8 14 20 26 (3rd row)

Since the sequence is going up by 6, write down your multiples of 6 on the 2nd row.

n 1 2 3 4 5 (1st row)

6n 6 12 18 24 30 (2nd row)

2 8 14 20 26 (3rd row)

Now, to get the numbers in the 3rd row from the 2nd row take off 4.

So, to get from the position numbers (n) to the numbers in the sequence you have to times the position numbers by 6 and take off 4.

Therefore, the nth term = 6n – 4.

If you want to find the nth term of a number sequence using the nth term formula then check out this article:

How to find the nth term of an increasing linear sequence.

Comments

Submit a Comment

  • profile image

    Sedzani 

    6 years ago

    What's value of a in this pattern 3a-4; 4a-3; 7a-6

  • profile image

    algebra.. 

    6 years ago

    THANK YOU WHOEVER YOU ARE!!! BECAUSE OF YOU I WILL NOT FAIL!!!! LOVE YOU!!!!!!!!! :D :D :D :D you teach even better than my teacher

  • profile image

    shit 

    6 years ago

    good

  • catman3000 profile imageAUTHOR

    Mark 

    6 years ago from England, UK

    Sheila, the nth term for your sequence in n^2. All you need to do is square the position number. 4^2 = 16, 5^2 = 25 and 50^ = 2500.

  • profile image

    sheila 

    6 years ago

    (1ST row) 1 2 3 4 5.....50

    (3rd row) 1 4 16 ( ), ( )......( )

  • profile image

    jimmy 

    6 years ago

    i don't get it

  • profile image

    ramina kate 

    6 years ago

    i cant understand

  • profile image

    blah blah blah 

    7 years ago

    this method really helps me :)

  • profile image

    regine 

    7 years ago

    I realised that for mine, this does not work as the 2nd row answer has similar pattern to the 3rd row. Here's my sequence: 2, 4, 7, 11, 16, 22

  • Shahid Bukhari profile image

    Shahid Bukhari 

    7 years ago from My Awareness in Being.

    You've found it my friend ... its indeed "unth" ... Because, linear calculations, begin, and end, with the Infinite infesting the origins and the end ... because, there are no numbers which could define the Infinite ... "unth" is as good a phonetic symbol, as any Greek symbol.

  • catman3000 profile imageAUTHOR

    Mark 

    7 years ago from England, UK

    Follow the method above if your sequence is linear. A linear sequence will be increasing or decreasing by the same amount each time.

  • profile image

    boy 

    7 years ago

    i am trying to do maths homework on nth terms and my ks3 teacher has given me a patternin numbers for linear sequances. Do i just work it out the same way as normal numbers. thanx

  • catman3000 profile imageAUTHOR

    Mark 

    8 years ago from England, UK

    Yes it is possible but it will be a quadratic sequence you are looking at. I will publish an article soon on quadratic sequences.

  • profile image

    Girl 

    8 years ago

    what if you have a sequence which adds 1,2,3,4,5,6,7,8,9 etc. - is it possible to find thenth term, if so how?? thanx

working

This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, owlcation.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://owlcation.com/privacy-policy#gdpr

Show Details
Necessary
HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
LoginThis is necessary to sign in to the HubPages Service.
Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
AkismetThis is used to detect comment spam. (Privacy Policy)
HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
Features
Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
MavenThis supports the Maven widget and search functionality. (Privacy Policy)
Marketing
Google AdSenseThis is an ad network. (Privacy Policy)
Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
Index ExchangeThis is an ad network. (Privacy Policy)
SovrnThis is an ad network. (Privacy Policy)
Facebook AdsThis is an ad network. (Privacy Policy)
Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
AppNexusThis is an ad network. (Privacy Policy)
OpenxThis is an ad network. (Privacy Policy)
Rubicon ProjectThis is an ad network. (Privacy Policy)
TripleLiftThis is an ad network. (Privacy Policy)
Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
Statistics
Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)