Answer
$S_{5}=-\dfrac{33}{4}$
Work Step by Step
Using $S_{n}=\dfrac{a_1(1-r^n)}{1-r}$, the sum of the first $
5
$ terms of the sequence $
-12,6,-3,...
$ is
\begin{array}{l}
S_{5}=\dfrac{-12\left(1-\left( -\dfrac{1}{2} \right)^5\right)}{1-\left( -\dfrac{1}{2} \right)}\\\\
S_{5}=\dfrac{-12\left(\dfrac{33}{32}\right)}{\dfrac{3}{2}}\\\\
S_{5}=-\dfrac{33}{4}
.\end{array}