Answer
$-22$
Work Step by Step
The sum of the first $n$ terms can be computed as:
$S_n=\dfrac{a_1(1-r^{n})}{1-r}...(1)$
where, $a_1$ is first term and $r$ is the common ratio, $r$ and can be computed as the quotient of a term and the term preceeding it. In a geometric series the ratio between consecutive terms is constant.
In order to find that ratio we simply divide any two successive terms as:
$r=\dfrac{a_2}{a_1}=-2$
Plug $5$ for n and $-2$ for $a_1$ and $-2$ for $r$ in the equation (1) to obtain:
$S_n=\dfrac{-2(1-(-2)^{5})}{1+2}=-22$
Thus, the sum of the first $5$ terms is: $S_5=-22$
