ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Arithmetic Progression used to find the nth term

Updated on October 4, 2010

Arithmetic Progression as requested by baig772

 Arithmetic Progression

An arithmetic progression or arithmetic sequence are a sequence of numbers that increase or decrease by a common difference.

Solving arithmetic progression is interesting since we can find the nth term of a particular sequence in a much easier way.

Within this hub we shall cover the steps involved in progression solving for;

  • Finding the nth term
  • Find a chosen term as defined by the question
  • Finding the A.P.(arithmetic progression ) itself

The general form of an arithmetic sequence is;

a,  a + d,  a + 2d,  a + 3d,  a + 4d...

Where the  a   =  first term (number)

                   d  =  common difference

To find the nth term of an arithmetic sequence we use the following formula;

tn  =  a  +  (n - 1)  d

When we add or subtract any constant number with all the terms of the sequence, the arithmetic sequence remains an arithmetic sequence.

Example:

6, 8, 10, 12, 14, 16, 18….. is an A.P with a common difference 2.

Add 4 with all the terms, and we get,

10, 12, 14, 16, 18, 20, 22…. this is also an A.P with a common difference 2.

 

When we multiply or divide by a non-zero constant with the terms of a sequence, the arithmetic sequence remains an arithmetic sequence.

Example:

10, 20, 30, 40, 50, 60, 70…. Is an A.P with a common difference 10.

Multiply all the terms by 2 , and we get,

20, 40, 60, 80, 100, 120, 140…. this is also an A.P with a common difference 20.

 

Finding the nth term

 

( i )  The sequence terms of an A.P. are  1, 12, 23, 34 find the nth term

Therefore;

t=  a  +  (n - 1) d

a   =  1                         ( where a = the first term)

d   =  12 - 1 = 11        (where d = common difference)

t=  1 + (n - 1)  d

t=  1 + (n - 1) 11

t=  1 + 11n -  11

t=  11n - 10  (nth term)

 

( ii )  Find the 11th term of the sequence 1, 12, 23, 34

Therefore;

a = 1                     (first term)

d = 12 - 1 = 11    (common difference)

n = 11                  (number of term required)

 

tn  =  a  +  ( n - 1)  d

t11 = 1  +  (11 - 1)  x  11

      = 1  +   (10   x   11)

      = 1  +  110

t11 =  111

 

(iii)  Find the A.P. of a sequence when the 7th term is 67

                                                              and the 16th term is 166

 

Consider the A.P. in the form a,  a + d,  a + 2d,  a + 3d,  a + 4d......

Therefore;

 t=  a  +  6d  =  67

t16 =  a  + 15d = 166

t7 - t16  =   a  +  6d  =  67

             = - a  - 15d = -166

             =        -  9d =  -99        

 -9d  =  -99   =   11

-9          -9

 

d  =  11

 

Put   "d = 11"  into the t7 equation

 

a  +      6d        =  67

a  =  (6 x 11)   =  67

a  =      66        =  67

a  =     67  -  66  =  1

a  =  1

t1 =   a  =  1

t2 =   a  +  d  =  1  +    11        =  12

t3 =   a  + 2d = 1  + (2 x 11)   =  23

t4 =   a  + 3d = 1  = (3 x 11)   =  34

 

So terms for this A.P. sequence are;   1,   12,   23,   34

Comments

    0 of 8192 characters used
    Post Comment

    • t.elia profile imageAUTHOR

      t.elia 

      5 years ago from Northern Ireland

    • profile image

      LyCa'Zen 

      6 years ago

      Thank You!!!, sa mga aNsWer... heheheh

    • profile image

      jonas moyo 

      6 years ago

      hi guys you made my day, i did this 8 yrs ago and now you have refreshad my memory

    • t.elia profile imageAUTHOR

      t.elia 

      8 years ago from Northern Ireland

      Thanks for the acknowledgement claree. Glad to be of help to you.

    • profile image

      claree 

      8 years ago

      Thanks- this really helped me in my exam studies

    • t.elia profile imageAUTHOR

      t.elia 

      8 years ago from Northern Ireland

      I couldn't agree more billy, I really enjoy maths although Im a chef by trade. Thankyou for your kind remarks really appreciated.Will pop over to your site later as I find some of your topics a great read and very interesting.

      Thanks

    • billyaustindillon profile image

      billyaustindillon 

      8 years ago

      You have some great meths hubs. I do a lot of research with fractals, fibonacci and other works like Gann, Elliott and Murrey in the financial markets. Maths and nature are what makes those studies work and viable. There is nothing as clinical as maths.

    • t.elia profile imageAUTHOR

      t.elia 

      8 years ago from Northern Ireland

      baig772,

      Hope this helps and thanks for the request

      Telia

    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, hubpages.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://hubpages.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)