A ball is dropped from a height of 9 metres and rebounds to a height of 6 metres and then on each bounce rises to $\frac{2}{3}$ of the previous height. Find the total distance through which the ball moves before coming to rest.
I understand this question is about geometric series.
Thus $S_{\infty} = \frac{9}{1-2/3} = 27$
But the solution gives total distance = 2*27-9 = 45m
Why is not the answer 27m?