Question

Determine whether the sequence converges or diverges. If it converges, give the limit.9, 27, 81, 243, ...

Answer 1

Step-by-step explanation

The series is geometric in nature, having a common ratio of:

`r=(27)/(9)=3,\text{ r=}(81)/(27)=3`

The common ratio is equal to three.

The formula for a geometric sequence is cr^n where "c" is a constant and "r" is the common ratio, the expression is as follows:

=9(3)^n.

A geometric series converges only if the common ratio's absolute value is more than or equal to 1. It diverges if the ratio is greater than or equal to 1.

Since the ratio is 3, the sequence diverges.

In conclusion, the sequence diverges.