The sequence in the image appears to be:

$3, 6, 3, 6, \ldots, -9, -18$

To analyze this, let’s look at the sequence in two parts.

1. Repeating Pattern: The sequence begins with a repeating pattern of $3, 6, 3, 6, \ldots$. This could indicate an oscillating sequence where numbers alternate between 3 and 6.

2. End Values: Toward the end of the sequence, it changes to $-9$ and $-18$, which suggests a different rule, potentially involving a shift in the sequence pattern.

If there is a specific rule or question associated with this sequence, please clarify. Otherwise, we could interpret it as two sections:

• An initial repeating pattern of 3 and 6.
• A concluding part with $-9$ and $-18$, possibly suggesting a different rule or a continuation of a sequence with a negative multiplier.

Would you like more details on interpreting or extending this sequence?

Follow-Up Questions:

1. What is the rule governing the transition from positive to negative values in the sequence?
2. Is there an underlying function or recursive formula for this sequence?
3. How would we continue the sequence beyond $-18$?
4. Can we identify a real-world application where such alternating sequences appear?
5. Could this sequence be a result of combining two different arithmetic sequences?

Tip:

When examining sequences, look for patterns in sign, magnitude, or operations between terms to identify potential rules or formulas.