SOLUTION: Two terms of an arithmetic sequence are a9 = 85 and a30 = 295. Find a rule for the nth term.

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Question 388655: Two terms of an arithmetic sequence are a9 = 85 and a30 = 295. Find a rule for the nth term.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B9%5D=a%5B1%5D%2B%289-1%29%2Ad
1.85=a%5B1%5D%2B8d
.
.
2.295=a%5B1%5D%2B30d
Subtract eq. 1 from eq. 2,
a%5B1%5D%2B29d-a%5B1%5D-8d=295-85
21d=210
d=10
Then use either equation to solve for a%5B1%5D.
a%5B1%5D%2B80=85
a%5B1%5D=5
So then,
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
a%5Bn%5D=5%2B%28n-1%29%2810%29
a%5Bn%5D=5%2B10n-10
highlight%28a%5Bn%5D=10n-5%29