.
This is an infinite geometric series question with r=.8 and the coefficient equal to 12. Since r<1, this series converges and the ball actually travels a finite distance.
for |r|<1 that formula holds true, but in our case here, however I forgot that the ball bounces and falls so Soroban is correct
Hello, Sarah!
Let's baby-step our way through this . . .A ball is dropped from a height of 12 feet.
The ball hits the ground and rebounds 80% of the distance it falls each time.
In theory, how far will the ball travel before coming to rest?
It falls 12 feet.
. . Then it falls that distance.
. . Then it falls that distance.
. . Then it falls that distance.
And so on . . .
We can see that the total distance is:
. .
. .
The geometric series has first term , common ratio
. . Its sum is: .
Therefore: .