HELP...PLEASE A ball that bounces up half the distance from which it is dropped is released three metres from the floor. If it continues bouncing forever, what is the total distance it travels (in m)?

Step-by-step explanation:

This will be a sum of two geometric sequences, one for distance falling and one for distance rising. The sum of a geometric sequence is expressed as s=a(1-r^n)/(1-r) where a=initial term, r=common ratio, and n= number of terms.

For the falling distance we have

f=3(1-.5^n)/(1-.5) as n goes to infinity it is just f=3/(.5)

For rising distance we have

r=1.5(1-.5^n)/(1-.5) and again as n goes to infinity it is r=1.5/(.5)

So the total distance travelled is

d=f+r

d=3/0.5+1.5/0.5

d=6+3

d=9 meters