Three terms x, y and z are in A.P.. So they are related by the equation:
2z - x = y
2x - y = z
2y - z = x
2 (x + z) = y
From the given information
x, y, z are in A.P.
So,
y - x = z - y
⇒ 2y - z = x
Show that x2+xy+y2,z2+zx+x2 and y2+yz+z2 are consecutive terms of an A.P., if x,y and z are in A.P.