If $a, b, c$ are in G.P. and $a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}}$, then which one of the following is correct?

$2x= y + z$ $x^2=yz$ $\frac{1}{x}+\frac{1}{z}=\frac{2}{y}$ $2y=x+z$

$2y=x+z$

Let us consider that , $a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}} = k $ a = kx  ,  b = ky ,  c = kz As, a , b & c are in G.P. So, b² = ac (ky)² = kx × kz  k2y  =  k(x+z) So, 2y = x + z Ans :- (D)  2y = x + z