Geometric Patterns Worksheet #4: Identify number patterns and complete the sequences.

Let's solve each of the number pattern problems step by step.

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1. 7, 14, 21, 28, __, __, __

Pattern:
Each number increases by 7.
- 7 → 14 (+7)
- 14 → 21 (+7)
- 21 → 28 (+7)

So next:
- 28 + 7 = 35
- 35 + 7 = 42
- 42 + 7 = 49

✔ Answer: 35, 42, 49

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2. 15, 25, 35, __, __, __, __

Pattern:
Each number increases by 10.
- 15 → 25 (+10)
- 25 → 35 (+10)

So next:
- 35 + 10 = 45
- 45 + 10 = 55
- 55 + 10 = 65
- 65 + 10 = 75

✔ Answer: 45, 55, 65, 75

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3. 8, 12, 16, 20, __, __, __

Pattern:
Each number increases by 4.
- 8 → 12 (+4)
- 12 → 16 (+4)
- 16 → 20 (+4)

So next:
- 20 + 4 = 24
- 24 + 4 = 28
- 28 + 4 = 32

✔ Answer: 24, 28, 32

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4. 50, 48, 46, 44, __, __, __

Pattern:
Each number decreases by 2.
- 50 → 48 (−2)
- 48 → 46 (−2)
- 46 → 44 (−2)

So next:
- 44 − 2 = 42
- 42 − 2 = 40
- 40 − 2 = 38

✔ Answer: 42, 40, 38

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5. 99, 90, 81, 72, __, __, __

Pattern:
Each number decreases by 9.
- 99 → 90 (−9)
- 90 → 81 (−9)
- 81 → 72 (−9)

So next:
- 72 − 9 = 63
- 63 − 9 = 54
- 54 − 9 = 45

✔ Answer: 63, 54, 45

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6. 3, 6, 9, 12, 15, __, __

Pattern:
Increases by 3 each time.
- 3 → 6 (+3)
- 6 → 9 (+3)
- 9 → 12 (+3)
- 12 → 15 (+3)

So next:
- 15 + 3 = 18
- 18 + 3 = 21

✔ Answer: 18, 21

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7. 15, 30, 45, 60, __, __, __

Pattern:
Increases by 15 each time.
- 15 → 30 (+15)
- 30 → 45 (+15)
- 45 → 60 (+15)

So next:
- 60 + 15 = 75
- 75 + 15 = 90
- 90 + 15 = 105

✔ Answer: 75, 90, 105

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8. 40, 60, 80, __, __, __, __

Pattern:
Increases by 20 each time.
- 40 → 60 (+20)
- 60 → 80 (+20)

So next:
- 80 + 20 = 100
- 100 + 20 = 120
- 120 + 20 = 140
- 140 + 20 = 160

✔ Answer: 100, 120, 140, 160

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9. 80, 70, 60, __, __, __, __

Pattern:
Decreases by 10 each time.
- 80 → 70 (−10)
- 70 → 60 (−10)

So next:
- 60 − 10 = 50
- 50 − 10 = 40
- 40 − 10 = 30
- 30 − 10 = 20

✔ Answer: 50, 40, 30, 20

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10. 0, 11, 22, 33, __, __, __

Pattern:
Increases by 11 each time.
- 0 → 11 (+11)
- 11 → 22 (+11)
- 22 → 33 (+11)

So next:
- 33 + 11 = 44
- 44 + 11 = 55
- 55 + 11 = 66

✔ Answer: 44, 55, 66

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✔ Final Answers:

| # | Pattern | Missing Numbers |
|---|--------|------------------|
| 1 | +7 | 35, 42, 49 |
| 2 | +10 | 45, 55, 65, 75 |
| 3 | +4 | 24, 28, 32 |
| 4 | -2 | 42, 40, 38 |
| 5 | -9 | 63, 54, 45 |
| 6 | +3 | 18, 21 |
| 7 | +15 | 75, 90, 105 |
| 8 | +20 | 100, 120, 140, 160 |
| 9 | -10 | 50, 40, 30, 20 |
|10 | +11 | 44, 55, 66 |

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These are all arithmetic sequences, where each term changes by a constant difference. The key is to find that common difference and apply it to fill in the blanks.