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 meters

Explanation:

Answer 2

The total vertical distance down the ball has traveled when it hits the ground the fifth time is 19.375 meters

Explanation:

We are given

A ball is dropped from a height of 10 meters

So, first term is 10

`a_1=10`

Each time it bounces, it reaches 50 percent of its previous height

so,

`r=0.50`

n=5

now, we can use summation formula

`S_n=a_1((1-r^n)/(1-r) )`

now, we can plug values

`S_5=10((1-(0.5)^5)/(1-0.5) )`

`S_5=19.375`

So,

The total vertical distance down the ball has traveled when it hits the ground the fifth time is 19.375 meters