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

Let A, B be two numbers between 3 and 81 such that series    3, A, B,81  forms a GP.

Let a=first term and common ratio =r.

$\therefore a_4=a.r^{4-1}$

$81=3.r^{3}$

$27=r^{3}$

$r=3$

For $r=3$,

$A=ar=(3)(3)=9$

$B=ar^2=(3)(3)^2=27$

The, required numbers are 9,27.

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