Answer :
The number of people that would have become sick in total over an indefinite period of time is of:
7500.
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, meaning that each term is obtained by the multiplication of the previous term by the common ratio q.
The nth term of a geometric sequence is given by the rule presented as follows:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of an infinite sequence, as long as |q| < 1, is given by:
[tex]S = \frac{a_1}{1 - q}[/tex]
The first term and the common ratio in this problem are given as follows:
- [tex]a_1 = 3000[/tex], as 3000 people got sick during the first week.
- q = 0.6, as the number decayed by 40% each week, that is, it was multiplied by 0.6 each week.
Hence the total number of people who got sick is obtained as follows:
S = 3000/0.4 = 7500.
More can be learned about geometric sequences at https://brainly.com/question/24643676
#SPJ1
