Algebra help please

Question

A ball is dropped vertically from a height of 80 meters. After each bounce, the ball reaches a maximum height equal to 60 percent of maximum height of the previous bounce.

a) Write the first three terms of the sequence. Explain how you know what they are.

b) Find the height to the nearest tenth of a meter of the ball after eighth bounce. Show and explain your work.

Answer 1

A ball vertically dropped from a height of

After each bounce the ball reaches a maximum height is of height of the previous bounce.

After each bounce maximum height is 

General formula for After number of bounce maximum height is 

(a)

The First three terms of the sequence is

Substitute in the general formula for After number of bounce maximum height.

(b)

Find the Height of the ball after Eight bounce.

Substitute in the general formula for After number of bounce maximum height.