# How do you find the 10th term in the geometric sequence -2,6,-18,...?

$39366$
Formula for ${a}_{n}$th term geometric series: $a {r}^{n - 1}$, where $a$ is the first term and $r$ is the common ratio.
In the sequence $\left[- 2 , 6 , - 18 , \ldots\right]$
$a = - 2$ and $r = \frac{{a}_{2}}{{a}_{1}} = \frac{6}{- 2} = - 3$
$\therefore {a}_{10} = a {r}^{10 - 1} = - 2 \cdot - {3}^{9} = 39366$