Using an infinite geometric sequence, it is found that the total distance that the ball travels is of 180 feet.
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.
Considering q < 1, the sum of an infinite sequence is given by:
[tex]S = \frac{a_1}{1 - q}[/tex]
In this problem, the first term and the common ratio are given by:
[tex]a_1 = 60, q = \frac{2}{3}[/tex]
Hence the total distance traveled in feet is given by:
[tex]S = \frac{a_1}{1 - q} = \frac{60}{1 - \frac{2}{3}} = \frac{60}{\frac{1}{3}} = 180[/tex]
More can be learned about geometric sequences at https://brainly.com/question/11847927
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