Question

If $S$ is the sum of infinite GP & $a$is the first term, then the common ratio $r$ is given by:

• A. $\frac{a-S}{S}$
• B. $\frac{S-a}{S}$
• C. $\frac{a}{1-S}$
• D. $\frac{S-a}{a}$

Answer 1

The correct option is B

$\frac{S-a}{S}$

Explanation for the correct option

Given, $S$ is the sum of infinite GP & $a$ is the first term, then the common ratio $r$ .

We know that the sum of infinite GP is: $S=\frac{a}{1-r}$.

$\begin{array}{rcl}1-r& =& \frac{a}{S}\\ r& =& 1-\frac{a}{S}\\ r& =& \frac{S-a}{S}\end{array}$

Hence, option B is correct.