Question

If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then is common ratio is

• A. $\frac{1}{10}$
• B. $\frac{1}{11}$
• C. $\frac{1}{9}$
• D. $\frac{1}{20}$

Answer 1

The correct option is B

$\frac{1}{11}$

(b) $\frac{1}{11}$

Let the first term of the G.P. be a

Let its common ratio be r

According to the question, we have :

First term = 10 [Sum of all successive terms]

$a=10\left(\frac{ar}{1-r}\right)$

$\Rightarrow a-ar=10ar$

$\Rightarrow 11ar=a$

$\Rightarrow r=\frac{a}{11a}=\frac{1}{11}$