Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 20

$\dfrac{-3}{8}$

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. First term $a_1= \dfrac{-1}{8}$ and Common ratio $r=\dfrac{2}{3}$ The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$ Thus, $S_n=\dfrac{ \dfrac{-1}{8}}{1-( \dfrac{2}{3})}=\dfrac{ \dfrac{-1}{8} \times 3}{3-2}$ Hence, $S_n=\dfrac{-3}{8}$