Answer
$S_{\infty}=-25$
Work Step by Step
Using $S_{\infty}=\dfrac{a_1}{1-r}$, the sum of the infinite geometric sequence $
-20,-4,-\dfrac{4}{5},...
$ is
\begin{array}{l}
S_{\infty}=\dfrac{-20}{1-\dfrac{1}{5}}\\\\
S_{\infty}=\dfrac{-20}{\dfrac{4}{5}}\\\\
S_{\infty}=-25
.\end{array}