If are in A.P., then prove that are in A.P.

will be in A.P.
if will be in A.P.                (By adding 1 to each number)
if  will be in A.P.
if     will be in A.P.                   (By dividing each number a + b + c)
if       if   
if                              if        (b - a) (b + a) = (c - b) (c + b)
if     
if          are in A.P. which is true.
Hence, are in A.P.