Insert 10 A.M.’s between 5 and -17 and prove that their sum is ten times the A.M. between them.

Insert 3 A.M.’s between 3 and 19.

Find the A.M. between : 6 and -8.

Find the A.M. between : 3.7 and 5.5.

The A.M. between two distinct positive numbers is twice the G.M. between them. Find the ratio of the greater to the smaller.

Insert 10 arithmetic means between 2 and 57.

If the A.M. between pth and qth terms of an A.P. be equal to the A.M. between rth and sth terms of the A.P., show that p +q= r+s.

If a,b,c are in AP and p is the AM between a and b and q is the AM between b and c, then show that b is the AM between p and q.

A.M. between two numbers is 10 and their G.M is 8. Find the numbers.

Prove that the sum of n arithmetic means between two numbers is n times the single A.M. between them.