Question

A bouncy ball is dropped such that the height of its first bounce is 3.25 feet and each successive bounce is 71% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).

Answer 1

Using a geometric sequence, it is found that the height of the 7th bounce of the ball would be of 0.4 feet.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

$a_n = a_1q^{n-1}$

In which $a_1$ is the first term.

In this problem, the first bounce is 3.25 feet and each successive bounce is 71% of the previous bounce's height, hence the first term and the common ratio are given, respectively, by:

$a_1 = 3.25, q = 0.71$

Hence, the height of the nth bounce is given by:

$a_n = 3.25(0.71)^{n-1}$

Then, the height of the 7th bounce in feet is of:

$a_7 = 3.25(0.71)^6 = 0.4$

More can be learned about geometric sequences at https://brainly.com/question/11847927

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