Question

The first term of an infinite G.P. is twice of the sum of all the successive term then common ratio is

• A. $\frac{2}{5}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{1}{3}$

Let the G.P be $a,ar,a{r}^2,..........\infty$ where $|r|<1$

Using given condition $a=2(ar+a{r}^2+a{r}^3+......\infty )$

$\Rightarrow 1=2(r+r^2+r^3+.......\infty )=\frac{2r}{1-r}$

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

Hence, option 'C' is correct.