Question

If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is
(a) 1/10
(b) 1/11
(c) 1/9.
(d) 1/20

Answer 1

(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]
$$\begin{gathered} a=10\left(\frac{ar}{1-r}\right) \\ \Rightarrow a-ar=10ar \\ \Rightarrow 11ar=a \\ \Rightarrow r=\frac{a}{11a}=\frac{1}{11} \end{gathered}$$