The situation narrated above is a geometric sequence with first term equal to 10 and the common ratio equal to 0.87. Since there is no telling as to how low will the bounce be, the sequence is infinite.
The equation for the sum of the terms in an infinite geometric sequence with common ratio that is lesser than 1 is,
S = Ao/(1 - r)
Substituting,
S = (10 ft) / (1 - 0.87)
S = 76.923
We multiply the sum by two.
2S = 76.923 x 2 = 153.846
We subtract 10 from this because the first bounce does not travel twice.
ANSWER: 143.846 ft
