Question

Arithmetic and Geometric Sequences (Context).A bouncy ball is dropped such that the height of its first bounce is 6.75 feet and each successive bounce is 68% of the previous bounce's height. What would be the height of the 6th bounce of the ball?

Answer 1

We have:

Let b = bounce height = 6.75 feet

p = percent of bounce height = 68%

And the formula of the height of nth bounce is:

$h=b\cdot p^{n-1}$

Then for the 6th bounce:

$h=6.75\times0.68^{6-1}=6.75\times0.68^5=0.981$

Round to nearest tenth = 1.0

Answer: 1.0 feet