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

Let a1 and a2 be two numbers between 3 and 81 such that the series, 3, a1, a2, 81, forms a G.P.


Let a0 be the first term and r be the common ratio of the G.P.


∴81 = ar3


⇒81 = (3)r3


⇒ r3 = 27


∴ r = 3


a1 = a0r = (3) (3) = 9


a2 = a0 r2 = (3) (3)2 = 27


∴ The required two numbers are 9 and 27.


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