Answer:
[tex]a_n=10-7n[/tex]
Step-by-step explanation:
The explicit form for an arithmetic sequence is:
[tex]a_n=a_1+d(n-1)[/tex]
where [tex]a_1[/tex] is the first term and [ted]d[/tex] is the common difference.
The given sequence is arithmetic because term-previous term is the same per each pair of term and previous term.
That is the following holds:
-4-3=-11-(-4)=-18-(-11)
All of these differences are equal to -7, the common difference.
So let's fill in the explicit form:
[tex]a_n=3+-7(n-1)[/tex]
or
[tex]a_n=3-7(n-1)[/tex]
or
[tex]a_n=3-7n+7[/tex]
or
[tex]a_n=10-7n[/tex]
