Question

If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 125 : 152, then the common ratio r is

• A. $\frac{3}{5}$
• B. $\frac{5}{3}$
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$

Answer 1

The correct option is A $\frac{3}{5}$

Here $\frac{S_3}{S_6}=\frac{125}{152}$
$\Rightarrow \frac{a(r^3-1)(r-1)}{a(r^6-1)(r-1)}=\frac{125}{152}$
$\Rightarrow (r^3-1)152=125(r^6-1)$
$\Rightarrow r^3=\frac{27}{125}\Rightarrow r=\frac{3}{5}$