Question

Find the sum of a finite geometric series. A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height. The total vertical distance down the ball has traveled when it hits the ground the fifth time is meters.

Answer 1

19.375 m.

Explanation:

Before the first bounce it has travelled 10 meters.

Then after just hitting the ground the second time it has travelled 10 +1/2(10) = 15 m.

The common ratio is 0.5 and we want the sum of 5 terms

= a1 (1 - r^n) / (1 - r)

= 10 * (1 - 0.5^5) / (1 - 0.5)

= 19.375 m.