Answer
$S_{3}=\dfrac{56}{9}$
Work Step by Step
Using $S_{n}=\dfrac{a_1(1-r^n)}{1-r}$, the sum of the first $
3
$ terms of the sequence with $a_1=8$ and $r=-\dfrac{2}{3}$ is
\begin{array}{l}
S_{3}=\dfrac{8\left(1-\left(-\dfrac{2}{3}\right)^3\right)}{1-\left(-\dfrac{2}{3}\right)}\\\\
S_{3}=\dfrac{8\left(1+\dfrac{8}{27}\right)}{1+\dfrac{2}{3}}\\\\
S_{3}=\dfrac{8\left(\dfrac{35}{27}\right)}{\dfrac{5}{3}}\\\\
S_{3}=\dfrac{56}{9}
.\end{array}
