Answer
$S_{∞} = \frac{144}{5}$
Work Step by Step
Given $a_{1} = 24$ and $r = \frac{1}{6}$
Sum of the terms of an infinite geometric sequence
$S_{∞} = \frac{a1}{1-r}$
Substituting $a_{1}$and $r$ values
$S_{∞} = \frac{24}{1-\frac{1}{6}}$
$S_{∞} = \frac{24}{\frac{6-1}{6}}$
$S_{∞} = \frac{24}{\frac{5}{6}}$
$S_{∞} = 24 \times \frac{6}{5}$
$S_{∞} = \frac{144}{5}$
