Aball is dropped from a height of 10 feet. each time it drops h feet, it rebounds 0.87h feet. find the total distance traveled by the ball. (round your answer to two decimal places.)

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