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If x, y, z are in A.P. and A1is the A.M. of x and y, and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.
If x, y, z are in A.P. and A1is the A.M. of x and y, and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.
Arithmetic Progressions | CBSE | Class 11 | Exercise 19.6 | Maths | RD Sharma
If x, y, z are in A.P. and A1is the A.M. of x and y, and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.

Answer:

Given,

A1 = AM of x and y

A2 = AM of y and z

A1 = (x+y)/2

A2 = (y+x)/2

AM of A1 and A2 = (A1 + A2)/2

=> [(x+y)/2 + (y+z)/2]/2

=> [x+y+y+z]/2

=> [x+2y+z]/2

x, y, z are in AP, y = (x+z)/2

AM = [(x + z/2) + (2y/2)]/2

AM = (y + y)/2

AM = 2y/2

AM = y

Thus, proved.

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