The function that represents the arithmetic sequence 8, 1.5, –5, –11.5 is given by:
f(n) = f(n - 1) - 6.5, f(1) = 8.
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.
The sequence can also be represented by a recursive function, as follows:
[tex]f(n) = f(n - 1) + q, f(1) = a_1[/tex]
In this problem, the first term is of 8, while the common ratio is of q = -6.5, hence the function is:
f(n) = f(n - 1) - 6.5, f(1) = 8.
More can be learned about arithmetic sequences at https://brainly.com/question/23842987
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