Question

A golf ball is dropped from a height of 30 ft to the pavement, and the rebound is one fourth the distance it drops. if after each descent it continues to rebound one fourth the distance dropped, what is the distance the ball has traveled when it reaches the pavement on its tenth descent?

Answer 1

Sum of a geometric sequcne
the ratio is 1/4 the initial height is 30

but we double it because it bounces down then up

but it doesn't bounce up on the first bounce so minus 30


sum of a geometric sequence where the first term is a1 and common ratio is r is
$S_n=\frac{a_1(1-r^n)}{1-r}$
so

the distance it traveled after n bounces is
$S_n=2(\frac{30(1-(\frac{1}{4})^n)}{1-\frac{1}{4}})-30$

so for n=10
$S_{10}=2(\frac{30(1-(\frac{1}{4})^{10})}{1-\frac{1}{4}})-30$
$S_{10}=2(\frac{30(1-(\frac{1}{4^{10}}))}{\frac{3}{4}})-30$
use your calculator
$S_{10}=49.9999999999$

so it traveled about 50ft