If `1/(y+x), 1/(2y) and 1/(y+z)` 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. then x,y,z are in :

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 x, y, z are in A.P. and tan^(-1) x, tan^(-1) y and tan^(-1)z are also in A.P. then show that x=y=z and y≠0

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

If p, q, r are in A.P. while x, y, z are in G.P., prove that x^(q-r).y^(r-p).z^(p-q) =1 .

If 1/(x+y),1/(2y),1/(y+z) are three consecutive terms of an A.P., prove that x, y, z are three consecutive terms of a G.P.

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

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

Area of the triangle with vertices (a, b), (x_1,y_1) and (x_2, y_2) where a, x_1,x_2 are in G.P. with common ratio r and b, y_1, y_2 , are in G.P with common ratio s, is

If x,y,z are in AP and tan^(-1)x,tan^(-1)y,tan^(-1)z are also in AP, then