Show that `x^2+x y+y^2,z^2+xz+x^2, y^2+y z+z^2,` are consecutive terms of an A.P., if `x ,y and z` are in A.P.

Show that x^(2)+xy+y^(2),y^(2)+yz+z^(2), are consecutive terms of an A.P.if x,yandz are in A.P.

Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

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

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 log, y, log, x, log, z are in G.P. xyz 64 and x y, z' are in A.P., then

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