Answer:
[tex]a_n = -11 +3(n -1)[/tex]
Explanation:
The [tex]n[/tex]th term of an arithmetic sequence is explicitly defined as [tex]a_n = a_1 +d(n -1)[/tex] where [tex]a_1[/tex] is the first term of the sequence and [tex]d[/tex] is the the common difference.
From the given first five terms of the sequence we can see that the first term is [tex]11[/tex] so [tex]a_1 = 11[/tex].
The common difference, [tex]d[/tex], can be calculated by [tex]a_n - a_{n -1}[/tex] so we'll find the common difference of the given sequence by letting [tex]n = 2[/tex]
[tex]d = a_2 - a_{2 -1} \\d = a_2 -a_{1} \\d = -8 -(-11) \\ d = -8 +11 \\ d = 3[/tex].
Now let's plug everything we know.
[tex]a_1 = -11[/tex]
[tex]d = 3[/tex]
[tex]a_n = -11 +3(n -1)[/tex]
