Question

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

• A. $3/5$
• B. $5/3$
• C. $2/3$
• D. $3/2$

Answer 1

The correct option is A $3/5$

$S_3$ / $S_5$ = 125 / 152

a$(1-r^3)$ / 1 -r / a$(1-r^5)$ / 1 - r = 125 /152

$(1-r^3)$ / $(1-r^6)$ = 125 / 152

$(1-r^3)$ / $\left(1^2\right)$ - $(r^3{)}^2$ = 125 / 152

1 / $(1+r^3)$ = 125 /152

152 = 125 + 125 $r^3$

125$r^3$ = 27

$r^3$ = 27 / 152

$r^3$ = (3 / 5 ) $r^3$

r = 3/5