Question

If in infinite G.P. first term is equal to the twice of the sum of the remaining terms, then its common ratio is:

• A. $1$
• B. $2$
• C. $1/3$
• D. $-1/3$

Answer 1

Answer: (C)

$1/3$

$a,a{r}^2,a{r}^3$………..$a{r}^7$

Given $a=2(a{r}^2+a{r}^3+....a{r}^n)$

Infinite group $\to a{r}^2+a{r}^3+....a{r}^7=\frac{ar}{1-r}$

$a=2\left(\frac{ar}{1-r}\right)$

$a-ar=2ar$

$\text{/}a=3\text{/}ar$

$r=\frac{1}{3}$.