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

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) (1/2) (B) (1/4) (C) (1/8) (D) (4/5)

Tardigrade Admin · Accepted Answer

( a /1- r )= S ....(1) (3 a /1-( r )2)= S ⇒ (6 a /2- r )= S ....(2) From (1) and (2) we get, r=(4/5)

Q. 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

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{8}$

$\frac{4}{5}$

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