"The numbersx, y, zare succesive terms of a G.S ...." => y/x = z/y => y^2 = xz .... (1)

".... with the sum of the three terms equal to 9" => x + y + z = 9 .... (2)

"When taken in the ordery, x ,zthe numbers form an A.S." => x - y = z - x => 2x = y + z .... (3)

Solve equations (1), (2) and (3) simultaneously for x, y, z.