A ball is dropped from a height of 120 cm. Every time it hits the ground, it will rebound to half of its original height. What is the total distance the ball has travelled by the time it hits the ground for the 4th time?
120 on the first drop.
then 2*120(1/2)^n = 240/2^n on the nth bounce
This is just a GP with
a = 240
r = 1/2
so S = 240(1 - 1/2^4)/(1 - 1/2) = 450
But the first drop is only a one-way trip, so 450-120 = 330
Check:
120 + 2(120/2) + 2(120/4) + 2(120/8) = 330