Insert four G.M.'s between 2 and 486.

Insert three A.M.s between 11 and 14

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

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

Insert five numbers between 8 and 26 such that the resulting sequence is an AP.

Suppose a and b are two numbers whose A.M is A. Let G_1 and G_2 be two G.M.s between a and b. Prove that (G_1^2)/(G_2)+(G_2^2)/(G_1)=2A

Insert three numbers between 1 and 256 so that the resulting sequence is a GP.

Insert 4 geometric means between 4 and 972.

If n arithmetic means are inserted between 2 and 38 then the sum of the resulting series is obtained as 200 . Then find the value of n.

Insert 6 arithmetic means between 3 and 24.

n arithmetic means are inserted between x and 2y and then between 2x and y . If the rth means in each case be equal then find the ratio x/y.