Answer
$\approx 19$ ft,
$(\displaystyle \frac{3}{4})^{n}\cdot 80$
Work Step by Step
Initial height: $a=80$ ft.
Height after 1st bounce: $a_{1}=\displaystyle \frac{3}{4}(a)=\frac{3}{4}(80)$
Height after 2nd bounce: $a_{2}=\displaystyle \frac{3}{4}(a_{1})=(\frac{3}{4})^{2}(80)$
Height after $3rd$ bounce: $a_{3}=\displaystyle \frac{3}{4}(a_{2})=(\frac{3}{4})^{3}(80)$
$...$
This pattern defines $a_{n}$ as height after the (n-1)th bounce.
common ratio: $\displaystyle \frac{3}{4}$, first term: 80,
$a_{n}=(\displaystyle \frac{3}{4})^{n-1}\cdot 80$
Height after the 5th bounce$=a_{6}$
$a_{6}=(\displaystyle \frac{3}{4})^{5}(80)=\frac{3^{5}\cdot 80}{4^{5}}$
$=\displaystyle \frac{19440}{1024}=18.984375\approx 19$ ft
Height after the nth bounce$= a_{n+1}$
$a_{n+1}=(\displaystyle \frac{3}{4})^{n}\cdot 80$
