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.

Explore the sequence 9, 12, 18, 105 and learn how to analyze it using arithmetic and geometric progressions. This problem examines the differences and ratios between terms and looks for potential patterns. Suitable for students in Grades 6-8.

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