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

$\frac{3}{5}$

Given that $\frac{a+ar+a{r}^2}{a+ar+a{r}^2+a{r}^3+a{r}^4+a{r}^5}=\frac{125}{152}.$

$\Rightarrow \frac{1+r+r^2}{1+r+r^2+r^3+r^4+r^5}=\frac{125}{152}\text{i.e.,}\frac{1+r+r^2}{(1+r+r^2)+r^3(1+r+r^2)}=\frac{125}{152}\Rightarrow \frac{1}{1+r^3}=\frac{125}{152}\Rightarrow r^3=\frac{152}{125}-1=\frac{27}{125}\Rightarrow r=\frac{3}{5}$