Q. In a geometric progression (GP) the ratio of the sum of the first three terms and first six terms is 125:152 the common ratio is
A) $\frac{1}{5}$
B) $\frac{2}{5}$
C) $\frac{4}{5}$
D) $\frac{3}{5}$
Explanation
(d)
Since, $\frac{a + ar + ar^{2}}{a + ar + ar^{2} + ar^{3} + ar^{4} + ar^{5}} = \frac{125}{162}$
$\Rightarrow \frac{1 + r + r^{2}}{\left( 1 + r + r^{2} \right)\left( 1 + r^{3} \right)} = \frac{125}{162}$
$\Rightarrow 1 + r^{3} = \frac{152}{125}$
$\Rightarrow r^{3} = \frac{27}{125} = \left( \frac{3}{5} \right)^{3}$
$\Rightarrow \ r = \frac{3}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.