Question

If $S$ is the sum of an infinite GP, the first term $a$, 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

Answer: (B)

Sum of an infinite $GP=\frac{a}{1-r}=S$
$\Rightarrow$ $a=S(1-r)$
$\Rightarrow$ $a-S=-Sr$
$\Rightarrow$ $r=\frac{S-a}{S}$