SOLUTION: What is the 17th term in the arithmetic sequence in which a-sub-6 is 101 and a-sub-9 is 83? Thank you in advance for your help!

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Question 472771: What is the 17th term in the arithmetic sequence in which a-sub-6 is 101 and a-sub-9 is 83?
Thank you in advance for your help!
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
What is the 17th term in the arithmetic sequence in which a-sub-6 is 101 and a-sub-9 is 83? 
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

a%5B6%5D=a%5B1%5D%2B%286-1%29d

101=a%5B1%5D%2B5d

a%5B9%5D=a%5B1%5D%2B%289-1%29d

83=a%5B1%5D%2B8d

So we have this system of equations:

system%28101=a%5B1%5D%2B5d%2C83=a%5B1%5D%2B8d%29

Subtract the second equation from the 1st and get

18=-3d%7D%7D%0D%0A%0D%0A%7B%7B%7B-6=d

Substitute in

101=a%5B1%5D%2B5d

101=a%5B1%5D%2B5%28-6%29

101=a%5B1%5D-30

131=a%5B1%5D

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

a%5B17%5D=131%2B%2817-1%29%28-6%29

a%5B17%5D=131%2B%2816%29%28-6%29

a%5B17%5D=131-96

a%5B17%5D=35

As a check, here are the first 17 terms of the sequence:

131, 125, 119, 113, 107, 101, 95, 89, 83, 77, 71, 65, 59, 53, 47, 41, 35.

The 6th, 9th and 17th terms are red:

Edwin