Question

Find a formula for the general term a, of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) (3, 10, 17, 24,31,. J. 3 points CaE12 8 1016 My Notes As Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) lim an

Answer 1

• an = 3 +7(n -1)
• diverges, limit DNE

Explanation:

Given the sequence that starts 3, 10, 17, 24, 31, ..., you want a formula for the n-th term, and its sum if it converges.

N-th term

The terms of the sequence given have a common difference of 7. That means it is an arithmetic sequence. The n-th term is ...

an = a1 +d(n -1) . . . . . . . . where a1 is the first term and d is the difference

For first term 3 and common difference 7, the n-th term is ...

an = 3 +7(n -1)

Limit

An arithmetic sequence never converges. Its limit does not exist (DNE).