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

STATEMENT-1 : The sum of 100 arithmetic means between two given number 1000 and 3016 is 200800 and STATEMENT-2 : The sum of n arithmetic means between two given numbers is n^(th) power of their single A.M.

Find the single arithmetic mean between: 7 and 31

If p is the first of the n arithmetic means between two numbers and q be the first on n harmonic means between the same numbers. Then, show that q does not lie between p and ((n+1)/(n-1))^2 p.

Find the single arithmetic mean between: 6 and -18

The arithmetic mean between two numbers is A and the geometric mean is G. Then these numbers are:

Find the single arithmetic mean between: (a-b) and (a+b)

Suppose p is the first of n(ngt1) arithmetic means between two positive numbers a and b and q the first of n harmonic means between the same two numbers. The value of p is

Suppose p is the first of n(ngt1) arithmetic means between two positive numbers a and b and q the first of n harmonic means between the same two numbers. The value of q is

The arithmetic mean of first n odd natural numbers, is

The arithmetic mean of first n natural numbers, is