From the image, you are tasked with categorizing sequences into "Arithmetic sequences" or "Geometric sequences." Here's how to determine which category each sequence belongs to:

1. Arithmetic Sequences:

   • The difference between consecutive terms is constant.
   • Example: 2, 6, 10, 14 (common difference is +4).

2. Geometric Sequences:

   • The ratio between consecutive terms is constant.
   • Example: 6, 12, 18, 24 (common ratio is ×2).

Classification:

• 9, 11, 13, 15 → Arithmetic sequence (common difference: +2).
• 2, 6, 10, 14 → Arithmetic sequence (common difference: +4).
• 5, 20, 80, 320 → Geometric sequence (common ratio: ×4).
• 3, 9, 27, 81 → Geometric sequence (common ratio: ×3).
• 9, 18, 36, 72 → Geometric sequence (common ratio: ×2).
• 6, 12, 18, 24 → Arithmetic sequence (common difference: +6).

Would you like further details about these sequences or additional examples? Here are 5 related questions to explore:

1. What is the formula for the nth term of an arithmetic sequence?
2. How can you calculate the sum of a finite geometric sequence?
3. Can a sequence be both arithmetic and geometric? Why or why not?
4. How do you find the common ratio or common difference if only given part of a sequence?
5. What are some real-world applications of arithmetic and geometric sequences?

Tip: Arithmetic sequences are often used in evenly spaced scenarios, while geometric sequences appear in exponential growth or decay