Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) −6, 4, − 8/ 3 , 16 /9 , − 32/ 27 , ...
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
an =
4(ln(n))2
/5n

The equation for the general term of the sequence is:

The sequence converges to 0.

Step-by-step explanation:

First, we need to find the formula for the general term of the sequence, which is a geometric sequence, meaning that it has a common ratio, given by:

The equation of a geometric sequence has the following format:

In which is the first term.

In this question, we have that . So, the equation for the general term is:

To find if the sequence converges, we find the limit of as . So

A number between 0 and 1 elevated to infinity tends to 0, so the sequence converges to zero.