Q. 264.5( 53 Votes )

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

Answer :

Let a_{1} and *a*_{2} be two numbers between 3 and 81 such that the series, 3, *a*_{1}, *a*_{2}, 81, forms a G.P.

Let *a _{0}* be the first term and

*r*be the common ratio of the G.P.

∴81 = ar^{3}

⇒81 = (3)r^{3}

⇒ *r*^{3} = 27

∴ *r* = 3

a_{1} = *a _{0}r* = (3) (3) = 9

*a*_{2} = *a _{0} r*

^{2}= (3) (3)

^{2}= 27

∴ The required two numbers are 9 and 27.

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