Question

REALLY NEED HELP! PLEASE. (WILL GIVE MEDALS)

One day during practice, LeBron decided to collect some data on the height of a basketball’s bounce. He first dropped the basketball from an initial height of 24 feet. At its first bounce, he recorded that the ball reached a height of 12 feet. At its second bounce, he recorded a height of 6 feet, and so on. His data is displayed in the table below.

Starting height 24 feet
First bounce 12 feet
Second bounce 6 feet
Third bounce 3 feet
Fourth bounce 1.5 feet

Answer 1

1. If the ball were dropped from a different initial height, would the common ratio be different? Explain your reasoning.

2. What is the height of the ball on the fifth bounce? Use the geometric sequence formula, an = a1rn – 1 and show your work.

3. What is the total distance of the height the ball has traveled during the first five heights shown in the chart?
Use the geometric series formula, Sn = (a1 – a1rn) / (1 – r)
and show your work.