If ‘a', is the Arithmetic mean of b and c, 'b', is the Geometric mean of c and a, then prove that 'c' is the Harmonic mean of a and b.

If x, y, z are in arithmetic progression and a is the arithmetic mean of x and y and b is the arithmetic mean of y and z, then prove that y is the arithmetic mean of a and b.

If x, y, z are in arithmetic progression and a is the arithmetic mean of x and y and b is the arithmetic mean of y and z, then prove that y is the arithmetic mean of a and b.

If x, y, z are in arithmetic progression and a is the arithmetic mean of x and y and b is the arithmetic mean of y and z, then prove that y is the arithmetic mean of a and b.

A, B and C are distinct positive integers, less than or equal to 10. The arithmetic mean of A and B is 9. The geometric mean of A and C is 6sqrt(2) . Find the harmonic mean of B and C.

The arithmetic mean and geometric mean of two numbers are 14 and 12 respectively. What is the harmonic mean of the numbers

The arithmetic mean of 3a, 3b, 3c is __________

If the arithmetic mean between a and b equals n times their geometric mean, then find the ratio a : b.

if a ne b and a : b is the duplicate ratio of a + c and b + c , prove that 'c' is the mean proportional between 'a' and 'b' .

Consider two positive numbers a and b. If arithmetic mean of a and b exceeds their geometric mean by 3/2, and geometric mean of aand b exceeds their harmonic mean by 6/5 then the value of a^2+b^2 will be