The image you have uploaded contains a sequence of numbers and a recurrence relation. Let's break down what is present:

1. Number sequence: 0, 2, 4, 6, 8, _ _ - It appears to be an arithmetic progression where the difference between each term is +2.

2. Recurrence relation: You’ve written something that resembles a recurrence relation, specifically: $a_n = a_{n-1} \cdot (n)$ This means that each term is determined by multiplying the previous term by $n$ (where $n$ could represent the position in the sequence).

Completing the sequence:

The sequence 0, 2, 4, 6, 8 increases by 2 each time. Therefore, to fill in the blanks:

• After 8, the next number would be 10 (since $8 + 2 = 10$).
• After 10, the next number would be 12 (since $10 + 2 = 12$).

Recap:

The completed sequence is: $0, 2, 4, 6, 8, 10, 12$

Would you like more details on how arithmetic sequences or recurrence relations work?

Here are 5 questions you could explore next:

1. How do you formally define an arithmetic progression?
2. What is a general formula for the $n$-th term of an arithmetic sequence?
3. How does a recurrence relation work in generating sequences?
4. Can this pattern be modeled with a different type of sequence, like geometric progression?
5. How can you solve for unknown terms if the common difference is not given?

Tip: Arithmetic sequences can always be identified by a constant difference between consecutive terms.