Question

(39 points PLZ HELP)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 the ball has traveled when it hits the ground the fifth time is

Answer 1

Answer:

19.375 meters

Step-by-step explanation:

We are given that:

A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height.

We have to find the total vertical distance the ball has traveled when it hits the ground the fifth time.

It is a geometric series with first term(a)= 10

                   common ratio(r)=1/2=0.5

                   and no. of terms(n)= 5

We have to find the sum of this geometric series=  

$\dfrac{a\times (1-r^n)}{1-r}\\ \\=\dfrac{10\times (1-0.5^5)}{1-0.5}\\ \\=\dfrac{10\times 0.96875}{0.5}\\ \\=19.375$

Hence, The total vertical distance the ball has traveled when it hits the ground the fifth time is:

  19.375 meters

Answer 2

So we need to find the sum of the first 5 terms.

You have told me that the first term is 10 meters, and that r = 0.5 per term.

With this knowledge, we can use the formula s_n=a₁((1-r^n)/(1-r)).

Plugging in the terms that we know...

s₅=10((1-0.5⁵)/(1-0.5))

s₅=10(0.96875/0.5)

s₅=10(1.9375)

s₅=19.375

With s₅, we can determine that the ball has traveled a total of 19.375 meters after 5 bounces.