Chapter 15.2, Problem 55E

To determine

To find: The sixth term of the sequence.

Answer to Problem 55E

The sixth term of the sequence is $a_n=\left(\frac{-1}{27}\right)$ .

Explanation of Solution

Given information:

The first term of a geometric sequence is $9$ .

The common ratio is $-\frac{1}{3}$ .

Calculation:

The $n^{th}$ term of a geometric sequence is.

  $a_n=a{n}^{n-1}$

Here, $a$ is the first term of the sequence and $r$ is the common ration.

  $a=9$ and $r=-\frac{1}{3}$

The $6^{th}$ term of the geometric sequence is.

  $\begin{array}{c}{a}_n=9{\left(\frac{-1}{3}\right)}^{6-1}\\ =\left(\frac{-9}{243}\right)\\ =\left(\frac{-1}{27}\right)\end{array}$

Therefore, the sixth term of the sequence is $a_n=\left(\frac{-1}{27}\right)$ .