Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - Guided Practice for Examples 1, 2, and 3 - Page 821: 4

$4$

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 $r=0.25$ from looking at the sequence, thus $|0.25|\lt1$. Hence the sum: $\dfrac{3}{1-0.25}=4$