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 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)/ra n dp ,q ,a n dr are in A.P., then prove that x ,y ,z are in H.P.

If (a-x)/(p x)=(a-y)/(q y)=(a-z)/ra n dp ,q ,a n dr are in A.P., then prove that x ,y ,z are in H.P.

If x,2y,3z are in A.P where the distinct numbers x,y,z are in G.P then the common ratio of G.P is

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 x ,2y ,3z are in A.P., where the distinct numbers x ,y ,z are in G.P, then the common ratio of the G.P. is a. 3 b. 1/3 c. 2 d. 1/2

If the 4th, 10th and 16th terms of a G.P. are x, y, and z respectively. Prove that x, y, z are in G.P.

If the 4^(t h) , 10^(t h) and 16^(t h) 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) are in A.P., then t a n x ,tany ,tanz are in (a)A.P. (b) G.P. (c) H.P. (d) none of these