Answer:
x = -7.5 - 1.5(n−1)
Step-by-step explanation:
the explicit formula for the arithmetic sequence has the form
x = a + d(n−1)
a is the first term and d is the common difference
The given arithmetic sequence is
-7.5,-9,-10.5,-12
The first term is -7.5
d = common difference = -9 - (-7.5) = -1.5
∴ x = -7.5 - 1.5(n−1)
The explicit formula for the arithmetic sequence shown in this problem is given by:
[tex]a_n = -6 - 1.5n[/tex]
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.
In this problem, the first term is -7.5 and each term is 1.5 less than the previous, hence:
[tex]a_1 = -7.5, d = -1.5[/tex]
And the formula is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
[tex]a_n = -7.5 - 1.5(n - 1)[/tex]
[tex]a_n = -6 - 1.5n[/tex]
More can be learned about arithmetic sequences at https://brainly.com/question/6561461
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