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Sum of n Terms

If 8 G.M.'s...

Question

If $8$ G.M.'s are inserted between $2$ and $3$ then the product of the $8$ G.M.'s is

A

6

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B

36

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C

216

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D

1296

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Solution

The correct option is D $1296$
$2, G_{1}, G_{2}, . . . . G_{8}, 3 - G . P$ $G_{i}$ are $G . M$

$G_{1}, G_{8} = G_{2} G_{7} = G_{3} G_{6} = G_{4} G_{5} = 2 \times 3 = 6$

$G_{1} G_{2} G_{3} G_{4} G_{5} G_{6} G_{7} G_{8} = 6 \times 6 \times 6 \times 6$

$= 1296$

$d$ is correct

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