ANSWER
[tex]a_n=7n - 22[/tex]
EXPLANATION
The recursive rule for the sequence is
[tex]a_n=a_{n-1}+7[/tex]
In general the recursive rule is written as:
[tex]a_n=a_{n-1}+d[/tex]
This implies that, d=7
The first term of the sequence is
[tex]a_1= - 15[/tex]
The explicit rule is given by:
[tex]a_n=a_1 + d(n - 1)[/tex]
We substitute to get;
[tex]a_n= - 15 + 7(n - 1)[/tex]
[tex]a_n= - 15 + 7n - 7[/tex]
[tex]a_n=7n - 22[/tex]
