Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 10

$\dfrac{88}{15}$

Each term of the sum is in the form $a_1r^{k-1}$, where $r=3/8$. Because $|r|=|3/8|<1$, the sum of the infinite geometric series exists. We calculate the sum: $$S=\dfrac{a_1}{1-r}=\dfrac{\dfrac{11}{3}}{1-\dfrac{3}{8}}=\dfrac{11}{3}\cdot \dfrac{8}{5}=\dfrac{88}{15}.$$