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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]

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