If x,1,z are in A.P. x,2,z are in G.P., show that `1/x,1/4,1/z` are in A.P.

If x, y, z are in A.P.; ax, by, cz are in GP. and 1/a, 1/b, 1/c are in A.P., then x/z+z/x is equal to

If a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.

If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,1/d ,1/e are in A.P. prove that a, c, e are in G.P.

If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,1/d ,1/e are in A.P. prove that a, c, e are in G.P.

If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,""1/d ,""1/e are in A.P. prove that a, c, e are in G.P.

Let a(a != 0) is a fixed real number and (a-x)/(px)=(a-y)/(qy)=(a-z)/(rz) . If p, q, r are in A.P., show that 1/x,1/y,1/z are in A.P.

If x, 1, z are in AP and x, 2, z are in GP, then x, 4, z will be in

If a ,\ b ,\ c are in A.P. b ,\ c ,\ d are in G.P. and 1/c ,1/d ,1/e are in A.P. prove that a ,\ c ,\ e are in G.P.?

If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove that x ,a n d4,z are in H.P.

If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove that x ,a n d4,z are in H.P.