Question

Am I right?

A basketball is dropped from an original height of 9 feet and on each bounce, bounces up 2/3 the distance it fell. How far will it have traveled by the time it hits the ground the 4th time?
I got 21.66667 by plugging it into the partial sum formula.

Answer 1

I think..... on first hit it will bounce 9×2/3=6 ft.....gain bounce 6×2/3= 4 ft.........third time....4×2/3=8/3.....and final......8/3×2/3=16/9...means 1.6 ft appropriate

Answer 2

1st drop:
drops: 9 feet
bounces back up: 6 feet
2nd drop:
drops: 6 feet
bounces: 4 feet
3rd drop:
drops: 4 feet
bounces: 2.66666feet
4th drop:
drops 2.6666
9+6+6+4+4+2.6666+2.6666=31.3 recurring