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: 1

$\frac{7}{2}$

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 $|\frac{3}{7}|\lt1$. Hence the sum: $\dfrac{2}{1-\frac{3}{7}}=\frac{7}{2}$