If a, b, c are in G.P. and `a^(1/x) =b^(1/y)=c^(1/z)` , prove that x, y , z are in A.P

IF a^(1/x)=b^(1/y)=c^(1/z) and abc=1 then x+y+z=…………..

a, b, c are in A.P. and x, y, z are in G.P. The points (a, x), (b, y), (c, z) are collinear if

If a, b, c are in A.P., a, x, b are in G.P. and b, y, c are in G.P. the point (x, y) lies on

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

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

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

If x = sum_(n = 0)^(infty) a^(n) , y = sum_(n = 0)^(infty) b^(n) , z = sum_(n=0)^(infty) c^(n) where a,b,c are in A.P . And |a| lt 1, |b| lt 1, |c| lt , then x,y,z, are in

If x gt 1, y gt 1 , z gt 1 are in G.P then (1)/(1 + log x ), (1)/( 1 + log y ), (1)/(1 + log z) are in

If a^(x) = b^(y) = c^(z) = d^(t) and a ,b ,c d are in G.P . Then x, y, z, t are in

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