SOLUTION: The first term of an arithmetic sequence is 9689 and the 100th term is 8996. a) Find the general term. b) Find the 110th term.

Algebra ->  Sequences-and-series -> SOLUTION: The first term of an arithmetic sequence is 9689 and the 100th term is 8996. a) Find the general term. b) Find the 110th term.       Log On


   

Question 1181277: The first term of an arithmetic sequence is 9689 and the 100th term is 8996.
a) Find the general term.
b) Find the 110th term.

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The first term of an arithmetic sequence is 9689 and the 100th term is 8996.
given:
a%5B1%5D=9689
a%5B100%5D=8996

a) Find the general term.
a%5Bn%5D=+a%5B1%5D%2Bd%28n-1%29
use given terms to fin common difference d
8996=+9689%2Bd%28100-1%29
8996-9689=d%2899%29
-693=d%2899%29
d=-693%2F99
d=+-7
the general term formula is
a%5Bn%5D=+9689-7%28n-1%29

b) Find the 110th term.
a%5B110%5D=+9689-7%28110-1%29
a%5B110%5D=+9689-7%28109%29
a%5B110%5D=+9689-763
a%5B110%5D=+8926

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
The first term of an arithmetic sequence is 9689 and the 100th term is 8996.
a) Find the general term.
b) Find the 110th term.
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            I will show you  HOW  TO  solve this problem easy and have fun (!) 


The distance between the first term and the 100-th term is

    9689 - 8996 = 693,


and there are 99 gaps of equal length between these points on the number line.


So, each gap is  693%2F99 = 7 units.


Thus the common difference of the AP is -7  (the progression decreases).


Now the general term  is   a%5Bn%5D = a%5B1%5D+%2B+%28n-1%29%2Ad = 9689 + (n-1)*(-7) = 9689 -7n + 7 = 9696 - 7n.    ANSWER


The 110-th term is  9696 - 110*7 = 8926.          ANSWER

Solved.