It looks like you've given a sequence of numbers: 9, 12, 18, 105. If you’re trying to find a pattern or rule behind this sequence, let's break it down step by step.

1. Differences between consecutive terms:
   • $12 - 9 = 3$
   • $18 - 12 = 6$
   • $105 - 18 = 87$

The differences don't follow a simple arithmetic progression.

2. Ratios between consecutive terms:
   • $\frac{12}{9} = 1.33$
   • $\frac{18}{12} = 1.5$
   • $\frac{105}{18} \approx 5.83$

The ratios also do not follow a clear geometric progression.

3. Observation: The jump from 18 to 105 is unusually large compared to the previous differences. This suggests that a different rule might apply for this sequence, or there may be multiple patterns combined.

Would you like to specify what kind of pattern or rule you're looking for? Or should I analyze this further for other possibilities?

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Would you like details on any part of the analysis?

Here are 5 related questions to consider:

1. What type of sequence are you trying to analyze (e.g., arithmetic, geometric, or something else)?
2. Are there any additional terms in this sequence?
3. Could this be a mixed pattern (e.g., involving both addition and multiplication)?
4. Is this sequence part of a larger problem, such as a word problem or puzzle?
5. Could this sequence involve modular arithmetic or another number theory concept?

Tip: Sometimes sequences combine both arithmetic and geometric properties, or introduce special operations at certain points. Always check for unusual jumps in the pattern.