If x, y, z are in A.P. and A 1 is the A.M. of x and y, and A 2 is the A.M. of y and z, then prove that the A.M. of A 1 and A 2 is y.

Question

Philoid · Accepted Answer

Given that,

A₁ = AM of x and y

And A₂ = AM of y and z

So,

AM of A₁ and A₂

Since x, y, z are in AP,

Finally, AM =

Hence proved.