Chapter 12 Sequences and Series - 12.5 Use Recursive Rules with Sequences and Functions - 12.5 Exercises - Quiz for Lessons 12.4-12.5 - Page 833: 2

$\frac{24}{11}$

An infinite geometric series has a sum if and only if $|r|\lt1$, where $r$ is the common ratio. It equals $\frac{a_1}{1-r}$ where $a_1$ is the first term. Here $|-\frac{5}{6}|\lt1$. Hence the sum: $\dfrac{4}{1-(-\frac{5}{6})}=\frac{24}{11}$