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

Answer: (A)

$\frac { 3 } { 5 }$

Answer 2

Here $\frac { S _ { 3 } } { S _ { 6 } } = \frac { 125 } { 152 } \Rightarrow \frac { a \left( r ^ { 3 } - 1 \right) / ( r - 1 ) } { a \left( r ^ { 6 } - 1 \right) / ( r - 1 ) } = \frac { 125 } { 152 }$

$\Rightarrow$ $\left( r ^ { 3 } - 1 \right) 152 = 125 \left( r ^ { 6 } - 1 \right) \Rightarrow r ^ { 3 } = \frac { 27 } { 125 } \Rightarrow r = \frac { 3 } { 5 }$ .