The explicit formula given is:

$a_n = 4 + (n-1) \cdot 6$

To write a recursive formula, we express $a_n$ in terms of the previous term $a_{n-1}$. Here's how we do it:

Step 1: General Pattern

Each term in the sequence increases by $6$ compared to the previous term. Thus: $a_n = a_{n-1} + 6$

Step 2: Specify the Base Case

The first term of the sequence is: $a_1 = 4$

Final Recursive Formula:

$a_n = a_{n-1} + 6, \quad \text{for } n \geq 2$ $a_1 = 4$

Would you like to see this formula applied to specific values, or do you have any questions?

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Here are 5 questions that expand on this concept:

1. How can you convert other explicit formulas into recursive formulas?
2. What is the advantage of using a recursive formula instead of an explicit one?
3. How would you derive a closed-form expression from a recursive formula?
4. Can you graph this sequence to visualize its growth?
5. How does the rate of change in this sequence compare to other arithmetic progressions?

Tip: When writing recursive formulas, always include the base case, as it defines the starting point for the recursion!