If x1, x2, x3 as well as y1, y2, y3 are in GP with same common ratio, then the points Px1,y1, Qx2,y2 and Rx3,y3

Let r be the common ratio. Then,    x2=x1r, x3=x1r2, y2=y1r and y3=y1r2∴ y2−y1x2−x1=y1r−y1x1r−x1=y1x1and, y3−y2x3−x2=y1r2−y1rx1r2−x1r=y1x1So,Slope of PQ = Slope of QRHence, points P,Q,R are collinear.