Insertion of n arithmetic means between two terms

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

Insert 3 arithmetic means between 4 and 16

Insert four arithmetic means between 4 and 29

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

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

Insert 3 arithmetic means between 5 and 21.

Insert two arithmetic mean between 16 and 22.

Prove that the sum of n arithmetic means between two numbers in n xx 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.

Insert five arithetic means between 5 and 29.