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
X,y, and z are in G,P. Hence,
Y=xr,z=xr2
Also, x, 2y, and 3z zre in A.P. Hence,
4y=x+3z
⇒4xr=x+3xr2
⇒3r2−4r+1=0
⇒(3r−1)(r−1)=0
⇒r=1/3(r≠1is not possible as x,y,z are distinct)