If `y-z,2(y-a),y-x` are in H.P. prove that `x-a,y-a,z-a` are in G.P.

If reciprocals of (y-x),2(y-a), (y-z) are in A.P., prove that x-a,y-a,z-a are in G.P.

If reciprocals of (y-x),2(y-a), (y-z) are in A.P., prove that x-a,y-a,z-a are in G.P.

If reciprocals of (y-x),2(y-a),(y-z) are in A.P then prove that x-a, y-a, z-a are in G.P

If reciprocals of (x+y)/2,y, (y+z)/2 are in A.P., show that x,y,z are in G.P.

If a^(x) = b^(y) = c^(z) and a, b, c, are in G.P., prove that x, y, z are in H.P.

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

If (a-x)/(p x)=(a-y)/(q y)=(a-z)/(rz) and p ,q ,and r are in A.P., then prove that x ,y ,z are in H.P.

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

If the and and terms of a G.P.are x,y and z,respectively. Prove that x,y,z are in G.P.

If the 4^(th),10^(th) and 16^(th) terms of a G.P. are x,y and z respectively ,then prove that x,y,z are in G.P.P.