Question

If three geometric means be inserted between 2 and 32, then the third geometric mean will be.

• A. 8
• B. 4
• C. 16
• D. 12

Answer 1

Answer: (C)

16

Answer 2

$2 , g _ { 1 } , g _ { 2 } , g _ { 3 } , 32$ where

$a = 2 , a r = g _ { 1 } , a r ^ { 2 } = g _ { 2 } , a r ^ { 3 } = g _ { 3 }$ and$a r ^ { 4 } = 32$

Now $2 \times r ^ { 4 } = 32 \Rightarrow r ^ { 4 } = 16 = ( 2 ) ^ { 4 } \Rightarrow r = 2$ .

Then third geometric mean $= a r ^ { 3 } = 2 \times 2 ^ { 3 } = 16$.

Aliter : By formula, $G _ { 3 } = 2 \cdot \left( \frac { 32 } { 2 } \right) ^ { 3 / 4 } = 2 \cdot 8 = 16$ .