Number Patterns worksheet with fill-in-the-blank exercises for students to practice identifying and extending sequences.

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. Write the pattern rule (how the sequence progresses).

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#### 1. 2, 4, 6, 8, 10, 12

- Look at the differences:
4 - 2 = 2
6 - 4 = 2
8 - 6 = 2
So it increases by 2 each time.

- Next number: 12 + 2 = 14

✔ Next number: 14
✔ Rule: Add 2

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#### 2. 3, 6, 9, 12, 15, 18

- Differences:
6 - 3 = 3
9 - 6 = 3
So it increases by 3

- Next number: 18 + 3 = 21

✔ Next number: 21
✔ Rule: Add 3

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#### 3. 23, 20, 17, 14, 11, 8

- Differences:
20 - 23 = -3
17 - 20 = -3
So it decreases by 3

- Next number: 8 - 3 = 5

✔ Next number: 5
✔ Rule: Subtract 3

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#### 4. 4, 14, 24, 34, 44, 54

- Differences:
14 - 4 = 10
24 - 14 = 10
So it increases by 10

- Next number: 54 + 10 = 64

✔ Next number: 64
✔ Rule: Add 10

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#### 5. 52, 44, 36, 28, 20, 12

- Differences:
44 - 52 = -8
36 - 44 = -8
So it decreases by 8

- Next number: 12 - 8 = 4

✔ Next number: 4
✔ Rule: Subtract 8

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#### 6. 7, 14, 21, 28, 35, 42

- Differences:
14 - 7 = 7
21 - 14 = 7
So it increases by 7

- Next number: 42 + 7 = 49

✔ Next number: 49
✔ Rule: Add 7

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🔹 Part 2: Use the rule to complete the sequence

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 at 55
- Add 5:
55 → 60 → 65 → 70 → 75 → 80

✔ Answer: 70, 75, 80

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#### 2. Subtract 11: 88, 77, ____, ____, ____

- Start at 88
- Subtract 11:
88 → 77 → 66 → 55 → 44

✔ Answer: 66, 55, 44

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#### 3. Add 9: 0, ____, ____, ____, ____

- Start at 0
- Add 9:
0 → 9 → 18 → 27 → 36

✔ Answer: 9, 18, 27, 36

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✔ Final Answers:

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

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

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