Answer
$-0.4$
Work Step by Step
An infinite geometric series has a sum if and only if $|r|\lt1$, where $r$ is the common ratio. If it exists, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term.
Here $r=0.5,a_1=-0.2$
Thus $|0.5|\lt1$, hence the sum exists.
Hence the sum: $\dfrac{-0.2}{1-0.5}=-0.4$
