Question

If $s$ is the sum of an infinite G.P, the first term $a$ then the common ratio $r$ 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, The sum of infinite G.P $=s$.

First term$=a$ and common ratio $=r$.

We know that, sum of infinite series in G.P is given by:

$s=\frac{a}{1-r};a=\mathrm{First}\mathrm{term}\mathrm{and}\mathrm{r}=\mathrm{common}\mathrm{ratio}$.

$$\begin{gathered} \Rightarrow s(1-r)=a \\ \Rightarrow s-sr=a \\ \Rightarrow s-a=Sr \\ \Rightarrow \frac{s-a}{s}=r \end{gathered}$$

Hence, option (B) is correct.