Question

The sum of first three terms of a $G.P$ is to the sum of the first six terms as $125:152$. Find the common ratio of the $G.P$.

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

Answer 1

Answer: (A)

$\frac{3}{5}$

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