Question

If the sum of an infinite GP. is S. Now if the first term is multiplied by 3 and common ratio is reduced to its half then the sum of G.P. is still S, then the common ratio of the G.P. is

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{8}$
• D. $\frac{4}{5}$

Answer 1

Answer: (D)

$ \frac{ a }{1- r }= S$ ....(1)
$\frac{3 a }{1-\frac{ r }{2}}= S \Rightarrow \frac{6 a }{2- r }= S$ ....(2)
From (1) and (2) we get, $r=\frac{4}{5}$