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 value of 5 times of common ratio of the G.P.

Answer 1

Given $\frac{S_3}{S_6}=\frac{125}{152}$

$\Rightarrow \frac{a(r^3-1)/(r-1)}{a(r^6-1)/(r-1)}=\frac{125}{152}$ [Sum of GP $=\frac{a(r^n-1)}{r-1}$ when $r>1$]

$\therefore \frac{1}{r^3+1}=\frac{125}{152}$

or $152=125r^3+125\Rightarrow 125r^3=27\therefore r=\frac{3}{5}\cdot$

$\Rightarrow 5r=3$