The given sequence is $4, 8, 16, 32, \dots$, which is a geometric sequence. The terms are generated by multiplying the previous term by $2$.

Recursive Formula:

Let $a_n$ represent the $n$-th term of the sequence. The recursive formula is:

$a_1 = 4 \quad \text{(initial term)}$ $a_n = 2 \cdot a_{n-1} \quad \text{for } n \geq 2$

This means each term is obtained by multiplying the previous term by $2$, starting with $a_1 = 4$.

---

Do you want a detailed explanation of how this formula is derived or how to use it? Here are some related questions for practice:

1. Write the explicit formula for the sequence $4, 8, 16, 32, \dots$.
2. Find the 10th term of the sequence using the recursive formula.
3. Modify the recursive formula if the first term changes to $5$.
4. Derive a recursive formula for the sequence $3, 6, 12, 24, \dots$.
5. Determine whether $1024$ is a term in the sequence $4, 8, 16, 32, \dots$.

Tip: Recursive formulas are great for describing sequences step-by-step, but explicit formulas make it easier to find any term directly.