1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Arithmetic Sequence Series Problem

  1. Nov 16, 2004 #1
    Hi. Please explain to me how to do these three problems:

    1. The terms x+3, 3x-1, and 7x-2 are consecutive terms in an arithmetic sequence. Find x.

    2. The sum of the first twenty-eight terms of an arithmetic series if the sum of the first twelve terms is -72 and the sum of the first twenty-four terms is 144.

    3. Find a, d, and tn for this sequence: t4= -9 , t15 = -31
  2. jcsd
  3. Nov 17, 2004 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    The terms in an arithmetic sequence always vary by a constant:
    a+ r, a+ 2r, a+ 3r, etc so that subtracting and consecutive two terms gives r.

    1. Here we must have (3x-1)- (x+1)= r= (7x-2)- (3x-1). Ignore the r and solve for x.

    2. With an arithmetic sequence you can find the "average" of all numbers by averaging the first and last terms of the sequence. The sum of n terms is just n times that average.

    In particular the average of the first 12 terms is (a1+ a12)/2 so the sum of the first 12 terms is 12(a1+ a12)/2= 6(a1+ a12)= -72.

    Similarly, the sum of the first 24 terms is 12(a1+ a24)= 144.

    Of course, if we take a1 as the first term and d as the common difference, a12= a1+ 11d and a24= a1+23d.
    Putting those into the two equations for the sums gives you 2 equations in the two unkowns, d and a1. Once you know those, you can calculate a28= a1+ 27d and the sum is 28(a1+ a28[/sub)/2= 14(a1+ a28).

    a1= a and ann= a+ (n-1)d so t4 (what I have called a4= a+ 3d= -9 and t15= a+ 14d= -31. Solve those two equations for a and d and then tn= a+ (n-1)d.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Arithmetic Sequence Series Problem
  1. Series and sequence (Replies: 3)

  2. Sequences and Series (Replies: 4)