The Total solution for NCERT class 6-12
If x, y, z are in A.P. and A1is the A.M. of x and y, and A2 isthe A.M. of y and z, then prove that the A.M. of A1 and A2 isy.
Given that,
A1 =AM of x and y
And A2 =AM of y and z
So, A1 =(x+y)/2
A2 =(y+x)/2
AM of A1 andA2 = (A1 + A2)/2
= [(x+y)/2 +(y+z)/2]/2
= [x+y+y+z]/2
= [x+2y+z]/2
Since x, y, z are inAP, y = (x+z)/2
AM = [(x + z/2) +(2y/2)]/2
= (y + y)/2
= 2y/2
= y
Hence proved.