Answer
$4$
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 $r=-\frac{3}{4},a_1=7$
Thus $|-\frac{3}{4}|\lt1$, hence the sum exists.
Hence the sum: $\dfrac{7}{1-(-\frac{3}{4})}=4$
