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Iteru [2.4K]
2 years ago
10

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 eac

h 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?
Mathematics
1 answer:
amm18122 years ago
7 0
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

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