Question

If the term of an infinite G.P. is equal to twice the sum of all the terms that follows it, then the common ratio is

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

Answer 1

Answer: (D)

$\frac {1} {3}$

Answer 2

By the given condition $a= 2\left[ar+ar^{2}+ar^{3}+.......\right]$ $\therefore a= 2 \frac{ar}{1-r}$ $\Rightarrow 1= \frac{2r}{1-r}$ $\Rightarrow 1-r = 2r$ $\Rightarrow 3r= 1$ $\Rightarrow r= \frac{1}{3}$ .