Question

If the sum of three terms of G.P. is 19 and product is 216, then the common ratio of the series is.

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

Answer 1

Answer: (B)

$\frac { 3 } { 2 }$

Answer 2

Let three terms of G.P. are $a , a r , a r ^ { 2 }$.

Then

$a + a r + a r ^ { 2 } = 19 \Rightarrow a \left[ 1 + r + r ^ { 2 } \right] = 19$ …..(i)

$a \cdot a r \cdot a r ^ { 2 } = 216 \Rightarrow a ^ { 3 } r ^ { 3 } = 216 \Rightarrow a r = 6$ …..(ii)

Dividing (ii) by (i),

$\frac { 6 } { r } + \frac { 6 } { r } r + \frac { 6 } { r } r ^ { 2 } = 19 \Rightarrow \frac { 6 } { r } + 6 + 6 r = 19$

$\Rightarrow r ^ { 2 } - \frac { 13 } { 6 } r + 1 = 0$. Hence $r = \frac { 3 } { 2 }$.