https://file.aiquickdraw.com/mathbot/file/1726495169474eij6tmlb.jpg

Let's analyze the sequences from the image to determine whether they are arithmetic and, if so, find the common difference.

1. **First sequence**: \(-2, -9, -16, -23, \dots\)
   - To check if this is arithmetic, find the difference between consecutive terms:
     - \(-9 - (-2) = -9 + 2 = -7\)
     - \(-16 - (-9) = -16 + 9 = -7\)
     - \(-23 - (-16) = -23 + 16 = -7\)
   - Since the difference is constant, this is an **arithmetic sequence** with a common difference \(d = -7\).

2. **Second sequence**: \(-2, 1, 4, 7, \dots\)
   - Checking the difference between consecutive terms:
     - \(1 - (-2) = 1 + 2 = 3\)
     - \(4 - 1 = 3\)
     - \(7 - 4 = 3\)
   - The difference is constant, so this is also an **arithmetic sequence** with a common difference \(d = 3\).

3. **Third sequence**: \(4, 12, 36, 108, \dots\)
   - Checking the difference between consecutive terms:
     - \(12 - 4 = 8\)
     - \(36 - 12 = 24\)
     - \(108 - 36 = 72\)
   - The difference is not constant. Hence, this is **not an arithmetic sequence**.

### Summary:
1. First sequence: **Arithmetic**, common difference \(d = -7\)
2. Second sequence: **Arithmetic**, common difference \(d = 3\)
3. Third sequence: **Not arithmetic**

Would you like more details or have any questions?

Here are 5 related questions:
1. What defines an arithmetic sequence?
2. How can you determine if a sequence is arithmetic?
3. What happens if the difference between consecutive terms isn't constant?
4. Can geometric sequences be confused with arithmetic sequences?
5. How is the common difference used in finding other terms in an arithmetic sequence?

**Tip:** In arithmetic sequences, the common difference is the amount added (or subtracted) to move from one term to the next.

For each sequence, determine whether it appears to be arithmetic. If it does, find the common difference.

Learn how to identify arithmetic sequences and find the common difference. This example involves three sequences where you need to check if the difference between consecutive terms is constant and solve for the common difference.

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