We have the arithmetic sequence:
12, 5, -2, -9, ...
We first need to know which is the common difference between the terms, clearly, it is -7.
Now we just need to use the formula below:
[tex]a_n=a_1+(n-1)d[/tex]
Where d is the common difference between the terms.
So we have:
[tex]a_n=12+(n-1)\times-7=-7n+19[/tex]
Then the correct answer is the recursive formula:
[tex]a_1=12[/tex]
[tex]a_n=a(n-1)-7[/tex]
