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

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#### Solution

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

⇒ *r*^{3} = 27

∴ *r* = 3 (Taking real roots only)

For *r* = 3,

*G*_{1} = *ar* = (3) (3) = 9

*G*_{2} = *ar*^{2} = (3) (3)^{2} = 27

Thus, the required two numbers are 9 and 27

Concept: Geometric Progression (G. P.)

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