When the ball is first dropped, it falls

feet. On the first bounce, it rebounds

feet, which means on the second "drop" it must travel

feet again. On the second bounce, the ball rebounds

feet, and on the third drop falls the same distance. And so on.
So there are two directions to track:


The total distance is the sum of these two:

Recall that for an infinite geometric sum, you have

provided that

. So the total distance traveled by the ball is

Starting with a height of

means the total distance is about 152.42 ft.