A rubber ball is dropped from a height of 10 feet onto a hard surface. After the first bounce, the ball is 6 feet in the air and continues to follow a sequence of bounces. Assume the distances from the ground form a geometric sequence. What is the total DOWNWARD vertical distance the ball has traveled after it hits the surface the 5th time?

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:

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:

A rubber ball is dropped from a height of 10 feet onto a hard surface.

This means that

The ball is 6 feet in the air and continues to follow a sequence of bounces

This means that

What is the total DOWNWARD vertical distance the ball has traveled after it hits the surface the 5th time?

This is . So

The total DOWNWARD vertical distance the ball has traveled after it hits the surface the 5th time is 23.056 feet.

you already gave the answer

step-by-step explanation: