ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Solving Arithmetic Sequences

Updated on April 27, 2011

SOLVING ARITHMETIC SEQUENCES

The following examples are problems involving arithmetic sequences. I included here several sample problems with their solutions.

Problem Number One :

If the first three terms of an arithmetic sequence are 2, 6 and 10, find the 40th term.

To solve the problem we use this formula for finding the nth term of an arithmetic sequence.

An = A + (n - 1) d

Where, An = is the nth term, in the case of our problem it is the 40th term

A = the first term of the sequence , in our problem it is 2.

n = number of terms, in our problem it is 40.

d = the interval of the terms, or the difference of the next term

from the previous term, To get d; d = 6 - 2 = 4.

Now, it is time to substitute the values to the formula for solving nth term where the 40th term is to be solved.

An = 2 + (40 - 1 ) 4

An = 2 + (39) 4

An = 2 + 156

An = 158.

The 40th term of the arithmetic sequence is 158.

Problem Number Two :

If the first term of an arithmetic sequence is -3 and the eighth term is 11, find d and write the first 10 terms of the sequence.

In this problem,

A = -3 n = 8 A8 = 11

If these values are substituted in the formula for An, we have

11 = -3 + (8 - 1) d

11 = -3 + 7d

14 = 7d

d = 2

The first ten terms are -3, -1, 1, 3, 5, 7, 9, 11, 13, 15

SUM OF AN ARITHMETIC SEQUENCE

The sum of the first n terms of an arithmetic sequence with first term A and nth term An is;

Sn = n/2 (A + An) or this formula maybe rewritten as

Sn = n {(A+An)/2}

It can be remembered easily in this form as : "the number of terms multiplied by the mean value or average of the first and last terms."

For an arithmetic sequence with the first term A and common difference d, the sum of the first n terms is ;

Sn = n/2 { 2a + (n - 1 ) d }

Problem Number Three :

Find the sum of all the odd integers from 1 to 1111, inclusive.

Solution :

Since the odd integers 1, 3, 5, etc, taken in order from the arithmetic sequence with d = 2, we can first find n from the formula for the nth term;

  • 1111 = 1 + (n - 1) 2

1111 = 2n -1

1112 = 2n

n = 556

S = 556/2 ( 1 + 1111)

= 278 ( 1112)

= 309, 136

Problem Number Four :

If A = 4, n = 10, A10 = 49; find d and Sn.

Substituting the given values for A, n, and An in the formula:

An = A + (n - 1) d, we get

49 = 4 + (10 - 1 ) d

49 = 4 + 9d

45 = 9d

d = 5

By using Sn = n {( A + An)/2}, we have

S10 = 10 { (4 + 49 )/2} = 5 * 53 = 265

Source :

COLLEGE ALGEBRA (tenth edition ) by :

Paul K. Rees

Fred W. Sparks

Charles Sparks Rees

Comments

    0 of 8192 characters used
    Post Comment

    • profile image

      rish 5 years ago

      Thank u vry max...

    • profile image

      cookiestsosie@yahoo.com 5 years ago

      i think this is cool

    • profile image

      DIWATANIANS 6 years ago

      WHOAH.... THANKS FOR HELPING MY ASSIGNMENT!

    • profile image

      mjean 6 years ago

      . tnx . u help me have my assignments and proje

      cts

    • profile image

      john 6 years ago

      hi```

    • profile image

      edjeboy desacula 6 years ago

      thanks God........... God bless

    • profile image

      jonna mae 6 years ago

      its easyto learn arithmetic sequence

    • profile image

      relente 6 years ago

      thank uo

    • profile image

      Kendall 6 years ago

      Thanks!

    • profile image

      Nevaeh 6 years ago

      Thaanks buddy : )

    • profile image

      Hiruy 6 years ago

      It's easy to learn sequence with out teacher ,so 10Q

    • profile image

      Rumy 6 years ago

      Yes, Its help me a lot.

      Thanks

    • profile image

      chi 7 years ago

      thank you!?

    • profile image

      nixie 7 years ago

      thank u for the information!

    • profile image

      That white guy 7 years ago

      Thanks this was incredibly helpfully for my 8th grade class homework now I can play black ops and reach lololololololololololol

      You see I can say all these stupid things because I will never be on this excact web page again...@.@:@:)-729'd

    • profile image

      ate mhae 7 years ago

      wow.... it is so very nice..! I love this one I understand now how to solve this simple math the arithmetic sequence... tnx.....

    • profile image

      sucks at mathalot:) 7 years ago

      Thanks so much you are the only one who I found that could help me with this stuff. I have a test coming up and this was much appreciative

      thanks a bundle :)

    • profile image

      salera gil john 8 years ago

      thank you for the write up.... it helps me a lot as a future teacher major in mathematics...

    • profile image

      luke 8 years ago

      hey azil its been 7 months...think u got blanked :)

    • profile image

      azil 8 years ago

      hi ms. cristina, what if i was asked to complete the sequence, for example:

      Complete the sequence 5 15 135 32805, if you don't mind, how should i answer that problem?

      Hope you can help me understand about this!

      Thanks in advance! =)

    • profile image

      Maria 9 years ago

      Thank for the formula of the sums!

    • profile image

      Cory 9 years ago

      this is the only site that explains it in a way i understand. thank you :)

    • profile image

      gfj 10 years ago

      nice

    • profile image

      morning star 10 years ago

      Thank you very much , you are so beautiful and attractive. I love you .

    • profile image

      jesusa 10 years ago

      thank you.................................................................

    • siddhinfo profile image

      Shrihari Sawant 10 years ago from Goa (India)

      Nice one really you have good write up.

    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"