https://file.aiquickdraw.com/mathbot/file/1730119755482tk5zgsfm.jpg

The sequence shown in the image is:

\[
3, 6, 3, 0, \dots, -9, -18
\]

This seems to follow a pattern, and we can analyze it step-by-step:

### Observing the pattern:
- From **3 to 6**, the change is \( +3 \).
- From **6 to 3**, the change is \( -3 \).
- From **3 to 0**, the change is \( -3 \).
- The next changes appear to continue decreasing.

Let's explore if the pattern follows arithmetic behavior:
- If we assume the **difference alternates** between increasing and decreasing by a fixed amount (perhaps \( -3 \) each time), it may continue like:
    - From \( 0 \to -3 \to -6 \to -9 \to -18 \).

This suggests the sequence could have **alternating behavior** with a fixed difference between terms. 

Would you like a detailed calculation for how the rest of the sequence might behave?

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### 5 Follow-up Questions:
1. Is this an arithmetic sequence, or could it be part of a more complex pattern?
2. What would be the next few terms of this sequence?
3. Can this sequence be expressed with a formula?
4. Could this be related to alternating series?
5. How would a graph of these points look?

**Tip:** When analyzing sequences, check for both arithmetic and geometric patterns for clues!

Find the pattern in the sequence: 3, 6, 3, 0, ..., -9, -18.

Explore the arithmetic pattern in the sequence 3, 6, 3, 0, ..., -9, -18. This problem focuses on sequence analysis, identifying differences, and predicting subsequent terms. Suitable for students in Grades 6-8.

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