If one geometric mean G and two arithmetic means p amd q be inserted between two quantities, then show that `G^(2)=(2p-q)(2q-p)`.

If one geometric mean G and two arithmetic means A_1 and A_2 be inserted between two given quantities, prove that : G^2=(2A_1-A_2)(2A_2-A_1) .

If one G.M., G and two A.M's p and q be inserted between two given numbers, prove that G^(2)= (2p-q) (2q-p)

Insert 10 arithmetic means between 2 and 57.

If G is the geometric mean between two distinct positive numbers a and b, then show that 1/(G-a)+1/(G-b)=1/G .

For an A.P., show that T_p+T_(p+2q)=2T_(p+q) .

If A, G and H are the arithmetic mean, geometric mean and harmonic mean between unequal positive integers. Then, the equation Ax^2 -|G|x- H=0 has

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.

The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean G satisfy the relation 2A+G^2=27. Find two numbers.

The geometric mean G of two positive numbers is 6 . Their arithmetic mean A and harmonic mean H satisfy the equation 90A+5H=918 , then A may be equal to:

If a is the A.M. of b and c and the two geometric means are G_(1) and G_(2) , then prove that G_(1)^(3)+G_(2)^(3) = 2abc