SOLUTION: Express the general term a(n), (with n as a subscript), for an arithmetic sequence whose 7th term is 11 and 20th term is -41. Then find the 9th term.

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Question 888309: Express the general term a(n), (with n as a subscript), for an arithmetic sequence whose 7th term is 11 and 20th term is -41. Then find the 9th term.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
General term of arithmetic sequence is a+(n-1)d using n as the index and d as the common difference.
The initial term is a.
n=7, term is 11;
n=20, term is -41.

a%2B%287-1%29d=11
a%2B6d=11
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a%2B%2820-1%29d=-41
a%2B19d=-41
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Start with Elimination Method to first find d.
1%2B19d-%28a%2B6d%29=-41-11
19d-6d=-52
13d=-52
highlight%28d=-4%29
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Using the n=7 equation, a=-6d%2B11
a=-6%28-4%29%2B11
highlight%28a=35%29

General term is highlight%28highlight%2835%2B%28n-1%29%28-4%29%29%29.
You can find whichever term you want.