Answer
$S_{\infty}=\dfrac{-5}{2}$
Work Step by Step
Using $S_{\infty}=\dfrac{a_1}{1-r}$, the sum of the infinite geometric sequence $
-3,\dfrac{3}{5},-\dfrac{3}{25},...
$ is
\begin{array}{l}
S_{\infty}=\dfrac{-3}{1-\left( -\dfrac{1}{5} \right)}\\\\
S_{\infty}=\dfrac{-3}{\dfrac{6}{5}}\\\\
S_{\infty}=\dfrac{-15}{6}\\\\
S_{\infty}=\dfrac{-5}{2}
.\end{array}