SOLUTION: For an arthmetic sequence with t6 = -24 and t14 = 6. Find S10. (6th term is -24, 14th term is 6, hence find the sum of the first 10 terms)

Algebra ->  Sequences-and-series -> SOLUTION: For an arthmetic sequence with t6 = -24 and t14 = 6. Find S10. (6th term is -24, 14th term is 6, hence find the sum of the first 10 terms)      Log On


   

Question 1108767: For an arthmetic sequence with t6 = -24 and t14 = 6. Find S10.
(6th term is -24, 14th term is 6, hence find the sum of the first 10 terms)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Eight common differences from n=6 to n=14

30%2F8=15%2F4=highlight_green%283%263%2F4%29

General term, A%2B%283%263%2F4%29%28n-1%29.

Find A, picking the n=6 term:
A%2B%283%263%2F4%29%285%29=-24
A=-24-5%283%263%2F4%29
A=-42%263%2F4
-
General Term, highlight_green%28-42%263%2F4%2B%283%263%2F4%29%28n-1%29%29

Sum the first 10 terms:
%2810%2F2%29%28-42%263%2F4%2B%28-42%263%2F4%2B%283%263%2F4%29%2A9%29%29
Simplify and compute this.