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If three geometric means be inserted between 2 and 32 , then the third geometric mean will be
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Verified Answer
The correct answer is:
$16$
$2, g_1, g_2, g_3, 32$ 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,
$G_3=2 \cdot\left(\frac{32}{2}\right)^{3 / 4}$ $=2 \cdot 8=16$
$a=2, a r=g_1, a r^2=g_2, a r^3=g_3$ 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,
$G_3=2 \cdot\left(\frac{32}{2}\right)^{3 / 4}$ $=2 \cdot 8=16$
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