Respuesta :
Answer:
The total DOWNWARD vertical distance the ball has traveled after it hits the surface the 5th time is 23.056 feet.
Step-by-step explanation:
Geometric sequence:
The nth term is a product of the previous(nth-1) term and the common ratio. That is:
[tex]a_n = qa_{n-1}[/tex]
In which q is the common difference.
Sum of the first n terms of geometric sequence:
The sum of the first n terms of a geometric sequence is given by:
[tex]S_n = \frac{a_1(1-q^n)}{1-q}[/tex]
A rubber ball is dropped from a height of 10 feet onto a hard surface.
This means that [tex]a_1 = 10[/tex]
The ball is 6 feet in the air and continues to follow a sequence of bounces
This means that [tex]q = \frac{6}{10} = 0.6[/tex]
What is the total DOWNWARD vertical distance the ball has traveled after it hits the surface the 5th time?
This is [tex]S_5[/tex]. So
[tex]S_5 = \frac{10(1-0.6^5)}{1-0.6} = 23.056[/tex]
The total DOWNWARD vertical distance the ball has traveled after it hits the surface the 5th time is 23.056 feet.
