Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

Let the two numbers between 3 and 81 be G1 and G2.

Thus 3, G1, G2, 81 are in G.P.

Let r be the common ratio.

Therefore ar3 = 81

or 3r3 = 81

or r3 = 27 or r = 3

or G1 = 3 × 3 = 9

G2 = 9 × 3 = 27

Hence the two required numbers are 9 and 27.

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