Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 13

$\dfrac{63}{17}$

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. First term $a_1= 7$ and Common ratio $r=\dfrac{-8}{9}$ The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$ Thus, $S_n=\dfrac{7}{1-(-8/9)}=\dfrac{7 \times 9}{9+8}$ Hence, $S_n=\dfrac{63}{17}$