Answer :
The explicit rule for the arithmetic sequence that represents the number of miles that Abby will run in week n is:
[tex]a_n = 15 + 2n[/tex]
Using this rule, it is found that she will run 39 miles during her 12th week of training.
What is an arithmetic sequence?
In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
On the first week, she runs 15 miles, and for each subsequent week this amount increases by 2 miles, hence the first term and the common difference are given as follows:
[tex]a_1 = 15, d = 2[/tex]
The explicit rule for the arithmetic sequence that represents the number of miles that Abby will run in week n is:
[tex]a_n = 15 + 2n[/tex]
During the 12th week, the number of miles that she will run is found as follows:
[tex]a_{12} = 15 + 2(12) = 39[/tex]
More can be learned about arithmetic sequences at https://brainly.com/question/28143210
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