SOLUTION: the sum of first six term of gp is -136.5 . if the common ratio is -2 . find the third term

Algebra ->  Finance -> SOLUTION: the sum of first six term of gp is -136.5 . if the common ratio is -2 . find the third term      Log On


   

Question 1140398: the sum of first six term of gp is -136.5 . if the common ratio is -2 . find the third term
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Apply the formula for the sum of the first n terms of a GP


    S[6] =  a%2A%28%28%28-2%29%5E6-1%29%2F%28-2-1%29%29 = a%2A%28%2864-1%29%2F%28-3%29%29 = - 21a.


where "a" is the first term of the GP.


Therefore,  -21a = -136.5,  a = %28-136.5%29%2F%28-21%29 = 6.5.


Then the third term of the GP is  a%5B3%5D = 6.5%2A%28-2%29%5E2 = 26.     ANSWER


--------------

On geometric progressions,  see introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Geometric progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.