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.

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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)   (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) Find the general term.

use given terms to fin common difference





the general term formula is


b) Find the th term.





Answer by ikleyn(52803)   (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.
~~~~~~~~~~~~


            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   = 7 units.


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


Now the general term  is    =  = 9689 + (n-1)*(-7) = 9689 -7n + 7 = 9696 - 7n.    ANSWER


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

Solved.



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