if a, b, c are in A.P. then solve that b+c-a,c+a-b,a+b-c are in A.P.

because of AP, c-b = b-a = d

b+c-a = c+b-a = c+d = b+2d
c+a-b = a+c-b = a+d = b
a+b-c = a-d = b-2d