If 1b+c,1c+a,1a+b are in A.P., then 9ax+1,9bx+1,9cx+1, x≠0 are in

2c+a=1b+c+1a+b=2b+a+c(b+c)(a+b)Cross multiply ⇒2ab+2b+2ac+2bc=2bc+2ac+c+2ab+a⇒2b=a+c∴a,b,c   are  in  A.P⇒ax,bx,cx   are   in  A.P⇒ax+1,bx+1,cx+1  are    in  A.P⇒9ax+1,9bx+1,9cx+1   are   in   G.P