Answer
$S_4=\dfrac{11}{3}$
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 $
\dfrac{1}{3},-\dfrac{2}{3},\dfrac{4}{3},...
$ is
\begin{array}{l}
S_4=\dfrac{\dfrac{1}{3}\left(1-(-2)^5\right)}{1-(-2)}\\\\
S_4=\dfrac{\dfrac{1}{3}(33)}{3}\\\\
S_4=\dfrac{11}{3}
.\end{array}