Suppose a, b, c are in A.P. and a2, b2, c2, are in G.P . If a

It is given that a, b, c are in A.P. ⇒2b=a+c⇒2b=32−b [∵a+b+c=32(Given)]⇒ b=12⇒a+c=1 [∵a+c=2b]It is also given that  a2,b2,c2 are in G.P.⇒b2=a2c2⇒b2=±ac⇒ac=±14 [∵b=12]CASE I: When ac =½  In this case, we have                 ac=14and a+c=1∴ a+14a=1⇒(2a−1)2=0⇒a=12               Thus, we have a = c =b =½ which is not possible as a