Year 6 Numeracy worksheet focusing on number sequences with missing numbers to complete.

Let's solve each of the number sequences step by step and determine the missing numbers and the rule for each.

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1) 5, 10, 20, ____, ____, ____, ____

- Pattern:
- 5 → 10 (×2)
- 10 → 20 (×2)
- So it’s multiplying by 2 each time.
- Next terms:
- 20 × 2 = 40
- 40 × 2 = 80
- 80 × 2 = 160
- 160 × 2 = 320

✔ Answer: 40, 80, 160, 320
✔ Rule: Multiply by 2

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2) -10, -25, -40, ____, ____, ____, ____

- Pattern:
- -10 → -25 (difference = -15)
- -25 → -40 (difference = -15)
- So it's subtracting 15 each time.
- Next terms:
- -40 – 15 = -55
- -55 – 15 = -70
- -70 – 15 = -85
- -85 – 15 = -100

✔ Answer: -55, -70, -85, -100
✔ Rule: Subtract 15

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3) 99, 91, 83, ____, ____, ____, ____

- Pattern:
- 99 → 91 (difference = -8)
- 91 → 83 (difference = -8)
- So it's subtracting 8 each time.
- Next terms:
- 83 – 8 = 75
- 75 – 8 = 67
- 67 – 8 = 59
- 59 – 8 = 51

✔ Answer: 75, 67, 59, 51
✔ Rule: Subtract 8

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4) 0.7, 0.9, 1.1, ____, ____, ____, ____

- Pattern:
- 0.7 → 0.9 (+0.2)
- 0.9 → 1.1 (+0.2)
- Adding 0.2 each time.
- Next terms:
- 1.1 + 0.2 = 1.3
- 1.3 + 0.2 = 1.5
- 1.5 + 0.2 = 1.7
- 1.7 + 0.2 = 1.9

✔ Answer: 1.3, 1.5, 1.7, 1.9
✔ Rule: Add 0.2

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5) 6.4, 6.9, 7.4, ____, ____, ____, ____

- Pattern:
- 6.4 → 6.9 (+0.5)
- 6.9 → 7.4 (+0.5)
- Add 0.5 each time.
- Next terms:
- 7.4 + 0.5 = 7.9
- 7.9 + 0.5 = 8.4
- 8.4 + 0.5 = 8.9
- 8.9 + 0.5 = 9.4

✔ Answer: 7.9, 8.4, 8.9, 9.4
✔ Rule: Add 0.5

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6) -52, -43, ____, ____, ____, ____

- Pattern:
- -52 → -43 (+9)
- So adding 9 each time.
- Next terms:
- -43 + 9 = -34
- -34 + 9 = -25
- -25 + 9 = -16
- -16 + 9 = -7

✔ Answer: -34, -25, -16, -7
✔ Rule: Add 9

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7) 420, 470, 520, ____, ____, ____, ____

- Pattern:
- 420 → 470 (+50)
- 470 → 520 (+50)
- Add 50 each time.
- Next terms:
- 520 + 50 = 570
- 570 + 50 = 620
- 620 + 50 = 670
- 670 + 50 = 720

✔ Answer: 570, 620, 670, 720
✔ Rule: Add 50

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8) 26, 66, 106, ____, ____, ____, ____

- Pattern:
- 26 → 66 (+40)
- 66 → 106 (+40)
- Add 40 each time.
- Next terms:
- 106 + 40 = 146
- 146 + 40 = 186
- 186 + 40 = 226
- 226 + 40 = 266

✔ Answer: 146, 186, 226, 266
✔ Rule: Add 40

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9) -3, -12, -21, ____, ____, ____, ____

- Pattern:
- -3 → -12 (-9)
- -12 → -21 (-9)
- Subtract 9 each time.
- Next terms:
- -21 – 9 = -30
- -30 – 9 = -39
- -39 – 9 = -48
- -48 – 9 = -57

✔ Answer: -30, -39, -48, -57
✔ Rule: Subtract 9

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10) 2, 6, 18, ____, ____, ____, ____

- Pattern:
- 2 → 6 (×3)
- 6 → 18 (×3)
- Multiply by 3 each time.
- Next terms:
- 18 × 3 = 54
- 54 × 3 = 162
- 162 × 3 = 486
- 486 × 3 = 1458

✔ Answer: 54, 162, 486, 1458
✔ Rule: Multiply by 3

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✔ Final Answers:

| Question | Missing Numbers | Rule |
|--------|------------------|------|
| 1) | 40, 80, 160, 320 | Multiply by 2 |
| 2) | -55, -70, -85, -100 | Subtract 15 |
| 3) | 75, 67, 59, 51 | Subtract 8 |
| 4) | 1.3, 1.5, 1.7, 1.9 | Add 0.2 |
| 5) | 7.9, 8.4, 8.9, 9.4 | Add 0.5 |
| 6) | -34, -25, -16, -7 | Add 9 |
| 7) | 570, 620, 670, 720 | Add 50 |
| 8) | 146, 186, 226, 266 | Add 40 |
| 9) | -30, -39, -48, -57 | Subtract 9 |
| 10) | 54, 162, 486, 1458 | Multiply by 3 |

> ✔ All sequences follow a consistent arithmetic or geometric pattern. The key is to find the difference or ratio between consecutive terms.

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