What's the next  3 numbers after 20,21,24  6,10,13  2,8,12  _,_,_?

To determine the next three missing numbers in the sequence, let's analyze the sequences provided:

- **Sequence 1:** 20, 21, 24
- **Sequence 2:** 6, 10, 13
- **Sequence 3:** 2, 8, 12

### Step-by-Step Analysis:

1. **Sequence 1:**
   - The difference between 21 and 20 is \(21 - 20 = 1\).
   - The difference between 24 and 21 is \(24 - 21 = 3\).

2. **Sequence 2:**
   - The difference between 10 and 6 is \(10 - 6 = 4\).
   - The difference between 13 and 10 is \(13 - 10 = 3\).

3. **Sequence 3:**
   - The difference between 8 and 2 is \(8 - 2 = 6\).
   - The difference between 12 and 8 is \(12 - 8 = 4\).

### Observations:

- The first differences between consecutive terms in each sequence are \(1\), \(4\), and \(6\).
- The second differences between consecutive terms in each sequence are \(3\), \(3\), and \(4\).

### Predicting the Next Sequence:

1. **First number:** 
   - Sequence 1: 20 → Sequence 2: 6 → Sequence 3: 2
   - The pattern seems to be decreasing. If we consider a decrease similar to the previous sequences, the next number could be around **0** or **1**.

2. **Second number:**
   - Sequence 1: 21 → Sequence 2: 10 → Sequence 3: 8
   - The differences between the terms are decreasing slowly, so the next number might be slightly higher than 8, possibly **6**.

3. **Third number:**
   - Sequence 1: 24 → Sequence 2: 13 → Sequence 3: 12
   - The differences between the terms are decreasing, so the next number might continue the trend and be around **10**.

### Final Prediction:
The next three numbers in the sequence could be **1, 6, 10**.

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Do you want details or have any questions?

Here are five related questions you might find interesting:
1. How can you identify patterns in decreasing sequences?
2. What strategies can be used to predict missing numbers in complex sequences?
3. What is the significance of second differences in sequence analysis?
4. How can sequences with non-linear patterns be solved?
5. What role do sequences play in calculus?

**Tip:** When analyzing sequences, consider both first and second differences. If the first differences aren't consistent, look at the second differences for a possible pattern.

Explore how to predict the next numbers in complex sequences with detailed step-by-step analysis. This problem covers sequence patterns, differences analysis, and predicting missing numbers. Suitable for students in Grades 7-9.

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