Let a,b,c be in A.P. and x,y,z be in G.P.. Then the points a,x, b,yand c,z will be collinear if

Given that a,b,c are in A.P.⇒   a−b=b−cNow, (a,x),(b,y) and c,z are collinear.⇒x−ya−b=y−zb−c⇒x−yy−z=a−bb−c=1⇒x−y=y−zSo, x,y are in A.P. Thus x,y,z are in A.P. and also in G.P,∴x=y=z