If a, b, c are in A.P., prove that:
a2 + c2 + 4ac = 2 (ab + bc + ca)
a2 + c2 + 2ac - 2ab - 2bc = 0
(a + c - b)2 – b2 = 0
a + c - b = b
a + c - 2b = 0
Since a, b, c are in AP
b - a = c - b
Hence proved