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Let five geometric means are inserted between $323$ and $2432$ then find the sum of all the geometric means.

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211

278

674

345

answer is A.

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Detailed Solution

Let the sequence of GM be

a, a r, a r 2, a r 3, a r 4, a r 5, a r 6, ...

. We know that,

a = 323

and

a r 6 = 2432

.
To find r, divide the sixth term by first term, we have

a r 6 a = 2432323 r 6 = 72964 r 6 = 3626 r = 32

Substitute the value of a and r in the sequence, and we have
Question Image

The formula for the sum of the geometric mean is given by,

S = a r n − 1 r − 1 = 16 325 − 1 32 − 1 = 16 24332 − 1 12 = 32 × 21132 = 211

Hence, the correct option is 1.

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