Follow the Rules: Number Patterns | Worksheet ... - Free Printable

Let's solve each part of the Number Patterns worksheet step by step.

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Part 1: Write the next number in each pattern. Then write the rule for the pattern.

#### 1. 5, 10, 15, 20, 25, ____
- Look at the differences:
- 10 – 5 = 5
- 15 – 10 = 5
- 20 – 15 = 5
- 25 – 20 = 5
- The pattern increases by +5.
- Next number: 25 + 5 = 30
- ✔ Next number: 30
- ✔ Rule: Add 5

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#### 2. 3, 6, 9, 12, 15, ____
- Differences:
- 6 – 3 = 3
- 9 – 6 = 3
- 12 – 9 = 3
- 15 – 12 = 3
- Increases by +3
- Next number: 15 + 3 = 18
- ✔ Next number: 18
- ✔ Rule: Add 3

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#### 3. 36, 30, 24, 18, 12, ____
- Differences:
- 30 – 36 = -6
- 24 – 30 = -6
- 18 – 24 = -6
- 12 – 18 = -6
- Decreases by –6
- Next number: 12 – 6 = 6
- ✔ Next number: 6
- ✔ Rule: Subtract 6

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#### 4. 7, 14, 21, 28, 35, ____
- Differences:
- 14 – 7 = 7
- 21 – 14 = 7
- 28 – 21 = 7
- 35 – 28 = 7
- Increases by +7
- Next number: 35 + 7 = 42
- ✔ Next number: 42
- ✔ Rule: Add 7

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#### 5. 20, 16, 12, 8, 4, ____
- Differences:
- 16 – 20 = -4
- 12 – 16 = -4
- 8 – 12 = -4
- 4 – 8 = -4
- Decreases by –4
- Next number: 4 – 4 = 0
- ✔ Next number: 0
- ✔ Rule: Subtract 4

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#### 6. 6, 12, 18, 24, 30, ____
- Differences:
- 12 – 6 = 6
- 18 – 12 = 6
- 24 – 18 = 6
- 30 – 24 = 6
- Increases by +6
- Next number: 30 + 6 = 36
- ✔ Next number: 36
- ✔ Rule: Add 6

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Part 2: Continue each pattern according to its rule.

#### 7. Rule: Add 9
Starts at: 0
- 0 + 9 = 9
- 9 + 9 = 18
- 18 + 9 = 27
- 27 + 9 = 36
- 36 + 9 = 45
- ✔ Pattern: 0, 9, 18, 27, 36, 45

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#### 8. Rule: Subtract 3
Starts at: 27
- 27 – 3 = 24
- 24 – 3 = 21
- 21 – 3 = 18
- 18 – 3 = 15
- 15 – 3 = 12
- ✔ Pattern: 27, 24, 21, 18, 15, 12

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#### 9. Rule: Add 8
Starts at: 0
- 0 + 8 = 8
- 8 + 8 = 16
- 16 + 8 = 24
- 24 + 8 = 32
- 32 + 8 = 40
- ✔ Pattern: 0, 8, 16, 24, 32, 40

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✔ Final Answers:

#### Part 1:
| Problem | Next Number | Rule |
|--------|-------------|------|
| 1 | 30 | Add 5 |
| 2 | 18 | Add 3 |
| 3 | 6 | Subtract 6 |
| 4 | 42 | Add 7 |
| 5 | 0 | Subtract 4 |
| 6 | 36 | Add 6 |

#### Part 2:
7. 0, 9, 18, 27, 36, 45
8. 27, 24, 21, 18, 15, 12
9. 0, 8, 16, 24, 32, 40

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📝 Explanation Summary:

- Finding the rule: Always look at the difference between consecutive numbers.
- Addition patterns: Numbers increase by a fixed amount.
- Subtraction patterns: Numbers decrease by a fixed amount.
- Once you identify the rule, apply it to find the next number or continue the sequence.

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