# The first term in a certain geometric sequence is x and the fourth term in the sequence is 27x, where x is a nonzero number. Which of the following represents the tenth term?

Apr 19, 2018

$\textcolor{b l u e}{x {\left(3\right)}^{9}}$

#### Explanation:

The nth term of a geometric sequence is given as:

$a {r}^{n - 1}$

Where:

$\boldsymbol{a}$ is the first term, $\boldsymbol{r}$ is the common ratio and $\boldsymbol{n}$ is the nth term.

First term is $x$

Fourth term is $27 x$

Using this:

$x {r}^{4 - 1} = 27 x$

${r}^{3} = 27$

$r = \sqrt[3]{{r}^{3}} = \sqrt[3]{27} = 3$

10th term:

${n}_{10} = x {\left(3\right)}^{10 - 1} = \textcolor{b l u e}{x {\left(3\right)}^{9}}$