SOLUTION: What is the nth term of the arithmetic sequence a[7]=34, a[18]=122?

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Question 598451: What is the nth term of the arithmetic sequence a[7]=34, a[18]=122?
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
the common difference is essentially the slope of an arithmetic progression.
a%5B7%5D=34, a%5B18%5D=122

leads us to
%0D%0Ad=%28a%5Bn%5D-a%5Bm%5D%29%2F%28n-m%29=%28122-34%29%2F%2818-7%29=8%0D%0A
We can rewrite the nth term as

%0D%0Aa%5B1%5D=a%5Bn%5D-%28n-1%29d%0D%0A


Now using the 7th term we write


%0D%0Aa%5B1%5D=34-%287-1%298=-14%0D%0A


nth term:

a%5Bn%5D=-14%2B%28n-1%298



:)