Number Patterns worksheet for practicing sequence extension and pattern recognition.

A worksheet titled "Number Patterns" with a cartoon character and ten numbered problems requiring students to extend number sequences.

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Show Answer Key & Explanations Step-by-step solution for: Number Patterns Worksheets

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Let's solve each number pattern step by step. The task is to extend the next two numbers and state the pattern rule for each sequence.

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1) 76, 70, 64, 58, 52, 46, 40

Step 1: Look at the differences between consecutive terms:
- 76 – 70 = 6
- 70 – 64 = 6
- 64 – 58 = 6
- 58 – 52 = 6
- 52 – 46 = 6
- 46 – 40 = 6

✔ Pattern: Subtract 6 each time.

Next two numbers:
- 40 – 6 = 34
- 34 – 6 = 28

✔ Answer:
Next two numbers: 34, 28
Pattern rule: Subtract 6

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2) 64, 69, 74, 79, 84, 89, 94

Differences:
- 69 – 64 = 5
- 74 – 69 = 5
- 79 – 74 = 5
- 84 – 79 = 5
- 89 – 84 = 5
- 94 – 89 = 5

✔ Pattern: Add 5 each time.

Next two numbers:
- 94 + 5 = 99
- 99 + 5 = 104

✔ Answer:
Next two numbers: 99, 104
Pattern rule: Add 5

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3) 73, 69, 65, 61, 57, 53, 49

Differences:
- 73 – 69 = 4
- 69 – 65 = 4
- 65 – 61 = 4
- 61 – 57 = 4
- 57 – 53 = 4
- 53 – 49 = 4

✔ Pattern: Subtract 4 each time.

Next two numbers:
- 49 – 4 = 45
- 45 – 4 = 41

✔ Answer:
Next two numbers: 45, 41
Pattern rule: Subtract 4

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4) 79, 71, 63, 55, 47, 39, 31

Differences:
- 79 – 71 = 8
- 71 – 63 = 8
- 63 – 55 = 8
- 55 – 47 = 8
- 47 – 39 = 8
- 39 – 31 = 8

✔ Pattern: Subtract 8 each time.

Next two numbers:
- 31 – 8 = 23
- 23 – 8 = 15

✔ Answer:
Next two numbers: 23, 15
Pattern rule: Subtract 8

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5) 23, 30, 37, 44, 51, 58, 65

Differences:
- 30 – 23 = 7
- 37 – 30 = 7
- 44 – 37 = 7
- 51 – 44 = 7
- 58 – 51 = 7
- 65 – 58 = 7

✔ Pattern: Add 7 each time.

Next two numbers:
- 65 + 7 = 72
- 72 + 7 = 79

✔ Answer:
Next two numbers: 72, 79
Pattern rule: Add 7

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6) 30, 32, 34, 36, 38, 40, 42

Differences:
- 32 – 30 = 2
- 34 – 32 = 2
- 36 – 34 = 2
- 38 – 36 = 2
- 40 – 38 = 2
- 42 – 40 = 2

✔ Pattern: Add 2 each time.

Next two numbers:
- 42 + 2 = 44
- 44 + 2 = 46

✔ Answer:
Next two numbers: 44, 46
Pattern rule: Add 2

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7) 67, 64, 61, 58, 55, 52, 49

Differences:
- 67 – 64 = 3
- 64 – 61 = 3
- 61 – 58 = 3
- 58 – 55 = 3
- 55 – 52 = 3
- 52 – 49 = 3

✔ Pattern: Subtract 3 each time.

Next two numbers:
- 49 – 3 = 46
- 46 – 3 = 43

✔ Answer:
Next two numbers: 46, 43
Pattern rule: Subtract 3

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8) 67, 62, 57, 52, 47, 42, 37

Differences:
- 67 – 62 = 5
- 62 – 57 = 5
- 57 – 52 = 5
- 52 – 47 = 5
- 47 – 42 = 5
- 42 – 37 = 5

✔ Pattern: Subtract 5 each time.

Next two numbers:
- 37 – 5 = 32
- 32 – 5 = 27

✔ Answer:
Next two numbers: 32, 27
Pattern rule: Subtract 5

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9) 56, 51, 46, 41, 36, 31, 26

Differences:
- 56 – 51 = 5
- 51 – 46 = 5
- 46 – 41 = 5
- 41 – 36 = 5
- 36 – 31 = 5
- 31 – 26 = 5

✔ Pattern: Subtract 5 each time.

Next two numbers:
- 26 – 5 = 21
- 21 – 5 = 16

✔ Answer:
Next two numbers: 21, 16
Pattern rule: Subtract 5

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10) 28, 31, 34, 37, 40, 43, 46

Differences:
- 31 – 28 = 3
- 34 – 31 = 3
- 37 – 34 = 3
- 40 – 37 = 3
- 43 – 40 = 3
- 46 – 43 = 3

✔ Pattern: Add 3 each time.

Next two numbers:
- 46 + 3 = 49
- 49 + 3 = 52

✔ Answer:
Next two numbers: 49, 52
Pattern rule: Add 3

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✔ Final Answers:

| # | Next Two Numbers | Pattern Rule |
|---|------------------|--------------|
| 1 | 34, 28 | Subtract 6 |
| 2 | 99, 104 | Add 5 |
| 3 | 45, 41 | Subtract 4 |
| 4 | 23, 15 | Subtract 8 |
| 5 | 72, 79 | Add 7 |
| 6 | 44, 46 | Add 2 |
| 7 | 46, 43 | Subtract 3 |
| 8 | 32, 27 | Subtract 5 |
| 9 | 21, 16 | Subtract 5 |
|10 | 49, 52 | Add 3 |

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Parent Tip: Review the logic above to help your child master the concept of pattern worksheet grade 9.

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