1. **State the problem:** Write a recursive formula for the sequence $6, 4, \frac{8}{3}, \frac{16}{9}, \ldots$. 2. **Identify the pattern:** To find a recursive formula, we need to find how each term relates to the previous term. 3. **Calculate the ratio between consecutive terms:** $$\frac{4}{6} = \frac{2}{3}, \quad \frac{\frac{8}{3}}{4} = \frac{8}{3} \times \frac{1}{4} = \frac{2}{3}, \quad \frac{\frac{16}{9}}{\frac{8}{3}} = \frac{16}{9} \times \frac{3}{8} = \frac{2}{3}$$ 4. **Observation:** Each term is multiplied by $\frac{2}{3}$ to get the next term. 5. **Write the recursive formula:** Let $a_n$ be the $n$th term. $$a_1 = 6$$ $$a_n = a_{n-1} \times \frac{2}{3} \quad \text{for } n \geq 2$$ 6. **Explanation:** The first term is 6, and each subsequent term is obtained by multiplying the previous term by $\frac{2}{3}$. **Final answer:** $$\boxed{a_1 = 6, \quad a_n = \frac{2}{3} a_{n-1} \text{ for } n \geq 2}$$