Geometric series?

Question

A ball is dropped from an initial height and allowed to bounce repeatedly. On the first bounce (one up-and-down motion), the ball reaches a height of 32 inches. On each successive bounce, the ball reaches 75% of its previous height. What is the total vertical distance that the ball travels in 10 bounces? (Do not include the initial height from which the ball is dropped.)

Answer 1

Yes, this is a geometric series:

 

64 + (0.75)(64) + (0.75)²(64) + ...

 

The series is geometric with common ratio r = 0.75.

 

Since -1 < r < 1, the series converges and has sum a/(1 - r), where a is the first term of the series.  

 

 The total distance travelled by the ball is 64/(1- 0.75) = 256"