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

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) (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):

RELATED QUESTIONS
The third term of an arithmetic sequence is -1 and the seventh term is -13; how would I... (answered by math_helper,ikleyn)

1) Use the explicit formula an=(-1)^n(13n-6), to find the first five terms of the... (answered by ikleyn)

Suppose that the eighth term of an arithmetic sequence is 59, and also suppose that the... (answered by mananth)

the third term of an arithmetic sequence is 9. The sum of the next two terms is -18. Find (answered by richwmiller)

Find both an explicit formula and recursive formula for the nth term for arithmetic... (answered by mathmate)

Write the first four terms of an arithmetic sequence whose ninth term is -51 and whose... (answered by rothauserc)

The twenty-third term in an arithmetic sequence is 2/3 and the fifty-third term in the... (answered by robertb)

Using the formula for the nth term of an arithmetic sequence, what is 101st... (answered by stanbon)