Question

A ball is dropped from a height of 48 feet. Each time the ball bounces, it travels back up half the distance from which it fell. How many feet has the ball traveled when it hits the ground from the fifth time?

Answer 1

1st drop : 48
1st bounce:24
2nd drop : 12
2nd bounce: 6 and so on and so forth:

This is a geometric progression with 1st term a = 48 and common ratio r= 1/2

The sum of all terms in a G.P is

S=a(1 - rⁿ⁻¹)/(1-r),
S = 48(1 - r⁴)/(1-r). Replace r by 1/2
S = 48[1-(1/2)⁴]/(1/2)

S = 90 ft