We are given the formula $s = \frac{a}{1-r}$ and are asked to find the value of $s$ when $a = 81$ and $r = \frac{1}{3}$.

1. Problem Description

We are given the formula $s = \frac{a}{1-r}$ and are asked to find the value of $s$ when $a = 81$ and $r = \frac{1}{3}$.

2. Solution Steps

We are given that $s = \frac{a}{1-r}$, $a = 81$, and $r = \frac{1}{3}$.

We substitute the given values of $a$ and $r$ into the formula for $s$:

$s = \frac{81}{1 - \frac{1}{3}}$

Now, we simplify the denominator:

$1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}$

So we have:

$s = \frac{81}{\frac{2}{3}}$

Dividing by a fraction is the same as multiplying by its reciprocal. So:

$s = 81 \cdot \frac{3}{2}$

$s = \frac{81 \cdot 3}{2}$

$s = \frac{243}{2}$

$s = 121.5$

3. Final Answer

The value of $S$ is $\frac{243}{2}$ or $121.5$.