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 then prove that x-a, y-a, z-a are in G.P

Suppose a is a fixed real number such that (a - x)/(px) = (a - y)/(qy) = (a - z)/(rz) If p,q,r, are in A.P., then prove that x,y,z are in H.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)/(px)=(a-y)/(qy)=(a-z)/(r) andp,q, andr are in A.P.,then prove that x,y,z are in H.P.

If x,1, and z are in A.P.and x,2, and z are in G.P.then prove that x, and 4,z are in H.P.

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

If sin(y+z-x),sin(z+x-y),sin(x+y-z) be in A.P.prove that tan x, tan y, tan z are also in A.P.