Question

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

Answer 1

Given that 3 and 81 are the first and fourth term of the G.P.

Let, G 1 and G 2 be the two numbers between 3 and 81 in G.P and r be the common ratio of the G.P.

Now, the n terms of G.P is,

T n =a r n−1

Now, the forth term of G.P from above equation is,

81=( 3 ) ( r ) 3 r 3 =27 r=3

Now, the term G 1 and G 2 is,

G 1 =ar G 2 =a r 2

Substitute the value of a and r, we get

G 1 =3×3 =9

G 2 =3× ( 3 ) 2 =3×9 =27

Thus, the required two numbers are 9 and 27.