Number sequences worksheet for practicing pattern recognition and arithmetic skills.

Let's solve each of the number sequences step by step and explain the pattern.

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1) 2, 4, __, 8

- Pattern: Increasing by 2.
- 2 → 4 (+2), so next should be 6, then 8.
- ✔ Answer: 6

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2) 1, 5, __, 13

- Differences: 5 - 1 = 4
- Try adding 4 again: 5 + 4 = 9
- Then 9 + 4 = 13 → matches!
- ✔ Answer: 9

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3) 3, 6, __, 12

- 3 → 6 (+3), so next is 9, then 12.
- ✔ Answer: 9

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4) 5, __, 15, 20

- 5 to 15 is +10, but with one missing number in between.
- Likely increasing by 5: 5 → 10 → 15 → 20
- ✔ Answer: 10

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5) 1, __, 9, 27

- Look at the pattern: 1, ?, 9, 27
- 27 is 3³, 9 is 3², 1 is 3⁰ → maybe powers of 3?
- But 3¹ = 3, so sequence: 3⁰=1, 3¹=3, 3²=9, 3³=27
- So missing number is 3.
- ✔ Answer: 3

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6) 4, __, 16, 32

- 4 → ? → 16 → 32
- 16 → 32 is ×2
- 4 → ? → 16 — likely ×2 each time?
- 4 × 2 = 8, 8 × 2 = 16, 16 × 2 = 32
- ✔ Answer: 8

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7) 6, 8, __, 20

- 6 → 8 (+2)
- Then skip a number to 20
- Let’s see: if it's increasing by 2s: 6, 8, 10, 12, ..., but 20 is too far.
- Maybe not arithmetic?

Try another idea:
- Could it be doubling? 6 → 8 (no), 8 → ? → 20
- 6, 8, ?, 20

Try differences:
- 8 - 6 = 2
- Suppose next difference is 4 → 8 + 4 = 12
- Then 12 to 20 is +8 → not consistent

Wait: 6, 8, 12, 20?

But let's look at this:

Maybe: 6, 8, 12, 20 — differences: +2, +4, +8 → doubling differences?

Yes! That works:
- +2, +4, +8 → geometric increase in differences
- So: 6 → 8 (+2), 8 → 12 (+4), 12 → 20 (+8)
- ✔ Answer: 12

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8) 4, 5, __, 10

- 4 → 5 (+1)
- Then to 10 — possibly +5?
- So maybe increasing by 1, then 2, then 3? Not clear.

Try: 4, 5, 7, 10 → differences: +1, +2, +3 → yes!
- 4 → 5 (+1), 5 → 7 (+2), 7 → 10 (+3)
- ✔ Answer: 7

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9) 4, 9, 16, __

- 4 = 2², 9 = 3², 16 = 4² → so next is 5² = 25
- ✔ Answer: 25

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10) 8, 27, 64, 125, __

- 8 = 2³, 27 = 3³, 64 = 4³, 125 = 5³ → so next is 6³ = 216
- ✔ Answer: 216

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11) 0, 1, 1, 2, 3, 5, __

- This is the Fibonacci sequence: each number is sum of two before it.
- 0, 1, 1, 2, 3, 5, ?
- 3 + 5 = 8
- ✔ Answer: 8

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12) 30, 28, 26, 24, __

- Decreasing by 2 each time
- 30 → 28 (-2), 28 → 26 (-2), 26 → 24 (-2), so next is 22
- ✔ Answer: 22

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13) 16, 12, 8, __

- Decreasing by 4 each time
- 16 → 12 (-4), 12 → 8 (-4), so next is 4
- ✔ Answer: 4

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14) 27, 26, 24, 21, __

- Differences:
- 27 → 26 (-1)
- 26 → 24 (-2)
- 24 → 21 (-3)
- So next: -4 → 21 - 4 = 17
- ✔ Answer: 17

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15) 32, 30, 26, 18, __

- Differences:
- 32 → 30 (-2)
- 30 → 26 (-4)
- 26 → 18 (-8)
- So next: -16 → 18 - 16 = 2
- Pattern: -2, -4, -8, -16 → doubling the subtraction
- ✔ Answer: 2

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16) 500, 100, 20, __

- 500 → 100: divide by 5
- 100 → 20: divide by 5
- So next: 20 ÷ 5 = 4
- ✔ Answer: 4

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17) 48, 24, 12, __

- Halving each time: 48 → 24 → 12 → 6
- ✔ Answer: 6

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18) 81, 27, 9, __

- 81 → 27: divide by 3
- 27 → 9: divide by 3
- So 9 → 3
- ✔ Answer: 3

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19) 256, 64, 16, __

- 256 → 64: divide by 4
- 64 → 16: divide by 4
- So 16 → 4
- ✔ Answer: 4

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✔ Final Answers:

1. 6
2. 9
3. 9
4. 10
5. 3
6. 8
7. 12
8. 7
9. 25
10. 216
11. 8
12. 22
13. 4
14. 17
15. 2
16. 4
17. 6
18. 3
19. 4

Let me know if you'd like these explained in a table or printed format!