Question 1116991
The first bounce(s1) it covers 10+(10/(5/3)) = 16 feet
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The second bounce(s2), it is (10/(5/3))+(10/(25/9)) = 9.6 feet
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The third bounce(s3), it is (10/25/9)+(10/(125/27)) = 5.76 feet and so forth
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The distance covered by each bounce is 3/5 the distance covered by the previous bounce
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The total distance covered is the sum of the partial sums,
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total distance = s1 + s2 + s3 + ...... + sn
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Note that the partial sums si form a geometric series where the common ratio is 3/5
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si = s1 * (3/5)^(n-1), where i = 1, n
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S(5) = 16 * (1 - (3/5)^5) / (1 - (3/5)) = 16 * (2882/3125) * (5/2) = 36.8896 feet
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Note the sum of the first n terms in a geometric sequence is
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S(n) = s(1) * (1 - r^n) / (1 - r), where s(1) is the first term and r is the common ratio, r not = 1
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