Follow the Rules: Number Patterns | Worksheet - Free Printable

Let's solve the Number Patterns worksheet step by step.

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🔹 Part 1: Find the next number and the rule

We are given sequences and need to:
1. Find the next number in the sequence.
2. Identify the pattern rule (e.g., add 2, multiply by 3, etc.).

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#### 1. 2, 4, 6, 8, 10, 12
- Look at the differences:
4 - 2 = 2
6 - 4 = 2
8 - 6 = 2
10 - 8 = 2
12 - 10 = 2
→ Each number increases by 2.

✔ Next number: 12 + 2 = 14
✔ Rule: Add 2

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#### 2. 3, 6, 9, 12, 15, 18
- Differences:
6 - 3 = 3
9 - 6 = 3
12 - 9 = 3
15 - 12 = 3
18 - 15 = 3
→ Increases by 3

✔ Next number: 18 + 3 = 21
✔ Rule: Add 3

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#### 3. 23, 20, 17, 14, 11, 8
- Differences:
20 - 23 = -3
17 - 20 = -3
14 - 17 = -3
11 - 14 = -3
8 - 11 = -3
→ Decreases by 3

✔ Next number: 8 - 3 = 5
✔ Rule: Subtract 3

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#### 4. 4, 14, 24, 34, 44, 54
- Differences:
14 - 4 = 10
24 - 14 = 10
34 - 24 = 10
44 - 34 = 10
54 - 44 = 10
→ Increases by 10

✔ Next number: 54 + 10 = 64
✔ Rule: Add 10

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#### 5. 52, 44, 36, 28, 20, 12
- Differences:
44 - 52 = -8
36 - 44 = -8
28 - 36 = -8
20 - 28 = -8
12 - 20 = -8
→ Decreases by 8

✔ Next number: 12 - 8 = 4
✔ Rule: Subtract 8

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#### 6. 7, 14, 21, 28, 35, 42
- Differences:
14 - 7 = 7
21 - 14 = 7
28 - 21 = 7
35 - 28 = 7
42 - 35 = 7
→ Increases by 7

✔ Next number: 42 + 7 = 49
✔ Rule: Add 7

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🔹 Part 2: Write the next number using the rule

Now we’re given a starting number and a rule. We apply the rule repeatedly.

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#### 1. Add 5: 55, 60, 65, ____, ____, ____
- Start: 55
- Add 5 → 60
- Add 5 → 65
- Next: 65 + 5 = 70
- Then: 70 + 5 = 75
- Then: 75 + 5 = 80

✔ Sequence: 55, 60, 65, 70, 75, 80

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#### 2. Subtract 11: 88, 77, ____, ____, ____
- Start: 88
- Subtract 11 → 77
- 77 - 11 = 66
- 66 - 11 = 55
- 55 - 11 = 44

✔ Sequence: 88, 77, 66, 55, 44

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#### 3. Add 9: 0, ____, ____, ____, ____
- Start: 0
- Add 9 → 9
- 9 + 9 = 18
- 18 + 9 = 27
- 27 + 9 = 36

✔ Sequence: 0, 9, 18, 27, 36

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✔ Final Answers:

#### Part 1:
1. 14, Add 2
2. 21, Add 3
3. 5, Subtract 3
4. 64, Add 10
5. 4, Subtract 8
6. 49, Add 7

#### Part 2:
1. 70, 75, 80
2. 66, 55, 44
3. 9, 18, 27, 36

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