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?

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!