From the recursive rule
[tex]a_n = a_{n-1}-13[/tex]
it follows that
[tex]a_{n-1}=a_{n-2}-13 \implies a_n = a_{n-2} - 2\times13[/tex]
[tex]a_{n-2}=a_{n-3}-13 \implies a_n = a_{n-3} - 3\times13[/tex]
and so on. Notice how the subscript on a on the right side and the coefficient multiplied by 13 add up to n (n - 2 + 2 = n; n - 3 + 3 = n; and so on). If we continue the pattern, we'll end up with
[tex]a_n = a_1 + (n-1)\times13[/tex]
so that the explicit rule for the n-th term in the sequence is
[tex]a_n = -2 + 13(n-1) \implies a_n = \boxed{13n-15}[/tex]
