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

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, y and z are in G.P, then show that logx, logy, logz are in A.P.

If distinct numbers x,y,z are in G.P. and 1/(x+a),1/(y+a),1/(z+a) are in A.P., prove that a=y .

a,b,x are in A.P.,a,b,y are in G.P. and a,b,z are in H.P. then:

If sin(y+z-x),sin(z+x-y),sin(x+y-z) are in A.P.then tan x,tan y, tan z are in (a)A.P.(b) G.P.(c) H.P.(d) none of these