To find the next number in the sequence, we should first analyze the pattern:

The sequence is: **12, 20, 24, 28, 34, 46, 76, ?**

1. **12 to 20:** +8
2. **20 to 24:** +4
3. **24 to 28:** +4
4. **28 to 34:** +6
5. **34 to 46:** +12
6. **46 to 76:** +30

To predict the next number, we observe that the differences between consecutive terms aren't consistent. However, let's analyze the pattern in the differences:

- **8, 4, 4, 6, 12, 30**

The pattern of differences increases irregularly, but we can hypothesize that the pattern involves some multiplication or addition by progressively larger values.

If we look closely:
- From 8 to 4, it's a decrease.
- From 4 to 6, it's an increase by 2.
- From 6 to 12, it's an increase by 6.
- From 12 to 30, it's an increase by 18.

Notice, 2, 6, 18 are multiplied by 3, indicating that the next difference might be 30 * 3 = 90.

So, if we add **90** to the last number in the sequence:

\[ 76 + 90 = 166 \]

Thus, the next number in the sequence is likely **166**.

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Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the sequence change if the differences followed a different pattern?
2. What are arithmetic and geometric sequences, and how do they differ from this sequence?
3. Can we find a formula to predict any term in this sequence?
4. What other types of sequences involve increasing or decreasing differences?
5. How can we use sequences in real-life applications?

**Tip:** When analyzing a sequence, always check the differences between terms first. If the differences aren't constant, consider the differences of the differences, as this might reveal a hidden pattern.

Learn how to analyze and predict the next number in the sequence 12, 20, 24, 28, 34, 46, 76, ? with a detailed step-by-step solution. This problem covers key concepts in number sequences and arithmetic sequences, examining irregular patterns in differences between terms.

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