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Sagot :
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:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] 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:
[tex]a_1 = 3.25, q = 0.71[/tex]
Hence, the height of the nth bounce is given by:
[tex]a_n = 3.25(0.71)^{n-1}[/tex]
Then, the height of the 7th bounce in feet is of:
[tex]a_7 = 3.25(0.71)^6 = 0.4[/tex]
More can be learned about geometric sequences at https://brainly.com/question/11847927
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