SOLUTION: In an arithmetic sequence, the third term is 1 and the ninth is 49. What is the explicit formula for the sequence?

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Question 1103556: In an arithmetic sequence, the third term is 1 and the ninth is 49. What is the explicit formula for the sequence?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The 9th term, 49, is 6 terms after the 3rd term, 1. So 49 is 1 plus 6 times the common difference. That means the common difference is (49-1)/6 = 8.

The first term is the 3rd term, minus 2 times the common difference: 1-2(8) = 1-16 = -15.

The first term is -15; the common difference is 8. The explicit formula for the sequence is

(first term) + ((n-1) times the common difference):
t%28n%29+=+-15%2B8%28n-1%29+=+-15%2B8n-8
or
t%28n%29+=+8n-23