Question

A ball is dropped from a height of 20 feet. Each time it bounces, it reaches ⅓ of its previous height. What is the total vertical distance the ball has traveled when it hits the ground the fourth time?

Answer 1

You have to calculate the sum of 20 + 20/3 + 20/ 9 + 20/27 + 20/ 81 + ...

That is a geometric series with first term 20 and r = 1/3.

Now you can use the formula for the sum of a geometric series:

∑ Ai from i = 0 to i = A / ( 1 - r), where A is the first term.

=> 20 + 20/3 + 20/ 9 + 20/27 + 20/ 81 + ... = 20 / ( 1 - 1/3) = 20 / (2/3) = 20*3/2 = 30.

Answer: 30 feet.