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Question

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

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Solution

Let G1 and G2 be two numbers between 3 and 81 such that the series 3,G1,G2,81, forms a G.P.

Let a be the first term and r be the common ratio of the G.P
81=(3)(r)3
r3=27
r=3
Forr=3,
G1=ar=(3)(3)=9
G2=ar2=(3)(3)2=27

Thus the required two numbers are 9 and 27.

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