Question 26

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

Let G1 and G2 be two numbers between 3 and 81 such that the series, 3, G1G2, 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 (Taking real roots only)

For r = 3,

G1 = ar = (3) (3) = 9

G2 = ar2 = (3) (3)2 = 27

Thus, the required two numbers are 9 and 27.