Question

please help
If a,b,c are in AP then Prove that
(a-c)^2 = 4(a-b)(b-c)

please this in detail

Answer 1

Given the three numbers are a b c are in ap so the numbers are e-d e and e+d.
Given lhs =(a-c) ^2
=(e-d-e-d) ^2
=(-2d) ^2
=4d^2
Rhs =4(a-b) (b-c).,. 1
We know that a-b=b-c=d...... 2
So from equation 1 and 2
Rhs =4d^2
Lhs is equal to rhs
Hence proved