Answer
$S_{\infty}=-20$
Work Step by Step
Using $S_{\infty}=\dfrac{a_1}{1-r}$, the sum of the infinite geometric sequence $
-10,-5,-\dfrac{5}{2},...
$ is
\begin{array}{l}
S_{\infty}=\dfrac{-10}{1-\dfrac{1}{2}}\\\\
S_{\infty}=\dfrac{-10}{\dfrac{1}{2}}\\\\
S_{\infty}=-20
.\end{array}