ANSWER
[tex]a_n = 11 - 3n[/tex]
EXPLANATION
The explicit rule for an arithmetic sequence is given by:
[tex]a_n = a_1 + d(n - 1)[/tex]
It was given that:
[tex]a_1 = 8[/tex]
and
[tex]a_2 = 3[/tex]
The common difference is
[tex]d = 5 - 8 = - 3[/tex]
We plug in the values into the explicit formula to get,
[tex]a_n = 8+ - 3(n - 1)[/tex]
Expand to get,
[tex]a_n = 8 - 3n + 3[/tex]
The explicit rule is
[tex]a_n = 11 - 3n [/tex]
