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: 19

$\frac{500}{3}$ in

This can be obtained by calculating the sum of an infinite geometric sequence. 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 $|0.85|\lt1$. Hence the sum: $\dfrac{25}{1-0.85}=\frac{500}{3}$