Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 16

$\dfrac{-8}{5}$

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. First term $a_1=-2$ and Common ratio $r=\dfrac{-1}{4}$ The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$ Thus, $S_n=\dfrac{-2}{1-(-1/4)}=\dfrac{-2 \times 4}{4+1}$ Hence, $S_n=\dfrac{-8}{5}$