Answer
$S_5=\frac{244}{27}\approx 9.04$
Work Step by Step
In a geometric series the ratio between consecutive terms is constant.
In order to find that ratio we simply divide any two subsessive terms:
$r=\frac{a_2}{a_1}=\frac{-4}{12}=-\frac{1}{3}$
The $S_n$, so the sum of the first n terms can be written as:
$S_n=a_1\times \frac{1-r^{n}}{1-r}$
Here, $n=5$, $a_1=12$, $r=-\frac{1}{3}$:
$S_n=a_1\times \frac{1-r^{n}}{1-r}$
$S_5=12\times \frac{1-(-\frac{1}{3}^{5})}{1-(-\frac{1}{3})}=12\times \frac{1+\frac{1}{243}}{1+\frac{1}{3}}=12\times \frac{\frac{244}{243}}{\frac{4}{3}}=12\times \frac{61}{81}=\frac{244}{27}\approx 9.04$
