Question

*Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 12 feet, then hits the floor and rebounds to 9.6 feet.
Write an explicit formula for the sequence.
Also, How high will the ball rebound after its fourth bounce?

Answer 1

Answer:

The explicit formula is $a_n=15(\frac{4}{5})^{n-1}$.

Step-by-step explanation:

First, we need to find the common ratio. We know this is a geometric sequence because the decrease from one term to the next is not a constant number.

To find the constant ratio, we can take the $2^{nd}$ term and divide by the $1^{st}$ term:

$\frac{2nd}{1st}=\frac{12}{15}=\frac{4}{5}$

So, our common ratio is $r=\frac{4}{5}$.

We already know our initial term, $a_0$ is 15, so we get:

$a_n=a_0(r)^{n-1}\\a_n=15(\frac{4}{5})^{n-1}$