Question

a tennis ball is dropped from a height of 30mtrs, and it rebounds four-fifths of the distance it has fallen after each fall. find
1. the height of nth bounce
2. the total distance traveled on rebound before coming to rest.

Answer 1

The nth bounce will have height 30 * (4/5)^n

No idea how many bounces it will take before stopping.

But, to get the total travel after n bounces, just add 30 to twice the sum of n terms of the sequence (a round trip is up and back down)

Answer 2

it's a convergent geometric series, so you can find the sum

the sum, minus 30, is the total rebound distance

s = a / (1 - r) = 30 / (1 - 4/5)