Number Patterns worksheet for practicing identifying and applying rules to number sequences.

Let's solve 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.

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#### 1. 5, 10, 15, 20, 25, ___
- Pattern: Each number increases by 5.
- Next number: 25 + 5 = 30
- Rule: Add 5 (or ×5, but here it's adding 5)
- ✔ Answer: 30; Rule: Add 5

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#### 2. 3, 6, 9, 12, 15, ___
- Pattern: Increases by 3 each time.
- Next number: 15 + 3 = 18
- Rule: Add 3
- ✔ Answer: 18; Rule: Add 3

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#### 3. 36, 30, 24, 18, 12, ___
- Pattern: Decreases by 6 each time.
- Next number: 12 - 6 = 6
- Rule: Subtract 6
- ✔ Answer: 6; Rule: Subtract 6

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#### 4. 7, 14, 21, 28, 35, ___
- Pattern: Increases by 7 each time.
- Next number: 35 + 7 = 42
- Rule: Add 7
- ✔ Answer: 42; Rule: Add 7

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#### 5. 20, 16, 12, 8, 4, ___
- Pattern: Decreases by 4 each time.
- Next number: 4 - 4 = 0
- Rule: Subtract 4
- ✔ Answer: 0; Rule: Subtract 4

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#### 6. 6, 12, 18, 24, 30, ___
- Pattern: Increases by 6 each time.
- Next number: 30 + 6 = 36
- Rule: Add 6
- ✔ Answer: 36; Rule: Add 6

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Part 2: Continue each pattern according to its rule.

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#### 7. Rule: Add 9
- Start: 0
- Pattern: 0, 9, 18, 27, 36, ...
- ✔ Answer: 0, 9, 18, 27, 36

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#### 8. Rule: Subtract 3
- Start: 27
- Pattern: 27, 24, 21, 18, 15, ...
- ✔ Answer: 27, 24, 21, 18, 15

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#### 9. Rule: Add 8
- Start: 0
- Pattern: 0, 8, 16, 24, 32, ...
- ✔ Answer: 0, 8, 16, 24, 32

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✔ Final Answers:

#### Part 1:
1. 30; Rule: Add 5
2. 18; Rule: Add 3
3. 6; Rule: Subtract 6
4. 42; Rule: Add 7
5. 0; Rule: Subtract 4
6. 36; Rule: Add 6

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

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✔ All patterns follow consistent arithmetic rules (addition or subtraction). The key is identifying the common difference between consecutive terms.

Let me know if you'd like this explained visually or with diagrams!