The ratio of the first to the last of n A.M.s between 5 and 35 is 1:4. Find n.

Insert 3 A.M.’s between 3 and 19.

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

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

There are n arithmetic means between 3 and 17. The ratio of the last mean to the first mean is 3: 1. Find the value of n.

If the ratio of sum of m terms of an A.P. to the sum of n terms is (2m + 1) : (3n +1), find the ratio of 7th to 10th term

n arithmetic means are inserted between 3 and 17 such that ratio of first and the last means is 1: 3, find n.

Find the sum S_n of the cubes of the first n terms of an A.P. and show that the sum of first n terms of the A.P. is a factor of S_n .

The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that a:b=(m+ sqrt(m^2-n^2)): (m-sqrt(m^2-n^2)) .

The ratio of the sums of m and n terms of an A.P. is m^2: n^2 . Show that the ratio of m^(th) and n^(th) term is (2m - 1 ) : (2n -1).

If G_1 is the first of n geometric means between a and b, show that : G_1^(n+1) =a^n b .