Question -
Answer -
Let’s assume G1 and G2 tobe two numbers between 3 and 81 such that the series 3, G1, G2,81 forms a G.P.
And let a bethe first term and r be the common ratio of the G.P.
Now, we have the 1st termas 3 and the 4th term as 81.
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
Therefore, the twonumbers which can be inserted between 3 and 81 so that the resulting sequencebecomes a G.P are 9 and 27.