Write linear function corresponding to the given sequence

Write a linear function that corresponds to the following arithmetic sequence: 8, 1, –6, –13, …

1. Find the common difference by subtracting two successive terms.
   
2. Confirm that the difference is the same between all of the terms.
   
3. Identify the first term $(a_1)$.
   
4. Write the explicit formula.
   
5. Simplify the explicit formula.
   
6. Write the formula in function notation.