The given recursive formula in the image is:

$a_1 = -8 \quad \text{and} \quad a_n = a_{n-1} - 5$

This is an arithmetic sequence where the first term $a_1 = -8$ and the common difference $d = -5$. The explicit formula for an arithmetic sequence is given by:

$a_n = a_1 + (n-1) \cdot d$

Substitute $a_1 = -8$ and $d = -5$ into this formula:

$a_n = -8 + (n-1)(-5)$

Simplifying:

$a_n = -8 - 5(n-1)$ $a_n = -8 - 5n + 5$ $a_n = -5n - 3$

Thus, the explicit formula is:

$a_n = -5n - 3$

Let me know if you want more details or if you have any questions!

Related Questions:

1. How do you derive the explicit formula for a recursive sequence?
2. What are the key differences between recursive and explicit formulas?
3. How do you verify the explicit formula for this sequence?
4. What is the 10th term of this sequence?
5. Can this formula be represented graphically, and what would the graph look like?

Tip: Always check that the explicit formula generates the same initial terms as the recursive sequence for verification.