1. **State the problem:** We have two sequences describing the number of stuffed frogs Janet and Patrick collect each month. We need to determine if each sequence is arithmetic or geometric, find the common difference or ratio, and provide a verbal description. 2. **Pattern 1 analysis:** The sequence is 3, 6, 9. - Check if arithmetic: Differences are $6-3=3$ and $9-6=3$, so the common difference is 3. - Check if geometric: Ratios are $\frac{6}{3}=2$ and $\frac{9}{6}=1.5$, not constant. - Conclusion: Pattern 1 is an arithmetic sequence with common difference 3. 3. **Pattern 2 analysis:** The sequence is 3, 6, 12. - Check if arithmetic: Differences are $6-3=3$ and $12-6=6$, not constant. - Check if geometric: Ratios are $\frac{6}{3}=2$ and $\frac{12}{6}=2$, constant ratio 2. - Conclusion: Pattern 2 is a geometric sequence with common ratio 2. 4. **Verbal descriptions:** - Pattern 1: The number of frogs increases by 3 each month. - Pattern 2: The number of frogs doubles each month. Final answers: - Pattern 1: Arithmetic sequence, common difference 3, increases by 3 frogs each month. - Pattern 2: Geometric sequence, common ratio 2, doubles the number of frogs each month.