Number Pattern Worksheets - Free Printable

Let's solve each of the number pattern problems step by step, identify the pattern rule, and then determine the next two numbers.

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1) 4, 8, 11, 22, 25, 50, 53, ___ , ___

Let’s look at the sequence:
- 4 → 8: ×2
- 8 → 11: +3
- 11 → 22: ×2
- 22 → 25: +3
- 25 → 50: ×2
- 50 → 53: +3

Pattern: Alternating between multiplying by 2 and adding 3.

So after 53:
- 53 × 2 = 106
- 106 + 3 = 109

✔ Next two numbers: 106, 109
✔ Rule: Multiply by 2, then add 3, repeat.

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2) 20, 15, 25, 20, 30, 25, 35, ___ , ___

Look at the sequence:
- 20 → 15: -5
- 15 → 25: +10
- 25 → 20: -5
- 20 → 30: +10
- 30 → 25: -5
- 25 → 35: +10

Alternating: -5, +10, -5, +10...

After 35:
- 35 - 5 = 30
- 30 + 10 = 40

✔ Next two numbers: 30, 40
✔ Rule: Subtract 5, then add 10, repeat.

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3) 48, 57, 65, 72, 78, 83, 87, ___ , ___

Differences between terms:
- 57 - 48 = 9
- 65 - 57 = 8
- 72 - 65 = 7
- 78 - 72 = 6
- 83 - 78 = 5
- 87 - 83 = 4

Decreasing by 1 each time: 9, 8, 7, 6, 5, 4

So next difference: 3 → 87 + 3 = 90
Then: 2 → 90 + 2 = 92

✔ Next two numbers: 90, 92
✔ Rule: Add decreasing numbers starting from 9 (9, 8, 7, 6, 5, 4, 3, 2...)

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4) 2, 4, 6, 12, 14, 28, 30, ___ , ___

Check differences:
- 2 → 4: +2
- 4 → 6: +2
- 6 → 12: ×2
- 12 → 14: +2
- 14 → 28: ×2
- 28 → 30: +2

Pattern: +2, +2, ×2, +2, ×2, +2

So after 30:
- 30 × 2 = 60
- 60 + 2 = 62

✔ Next two numbers: 60, 62
✔ Rule: Add 2, add 2, multiply by 2, repeat.

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5) 3, 6, 5, 10, 9, 18, 17, ___ , ___

Break it down:
- 3 → 6: ×2
- 6 → 5: -1
- 5 → 10: ×2
- 10 → 9: -1
- 9 → 18: ×2
- 18 → 17: -1

Pattern: ×2, -1, ×2, -1, ×2, -1

After 17:
- 17 × 2 = 34
- 34 - 1 = 33

✔ Next two numbers: 34, 33
✔ Rule: Multiply by 2, subtract 1, repeat.

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6) 53, 50, 47, 43, 40, 35, 32, ___ , ___

Differences:
- 53 → 50: -3
- 50 → 47: -3
- 47 → 43: -4
- 43 → 40: -3
- 40 → 35: -5
- 35 → 32: -3

Wait — not consistent. Let's check:

- 53, 50, 47 → -3, -3
- 47, 43 → -4
- 43, 40 → -3
- 40, 35 → -5
- 35, 32 → -3

Hmm — maybe alternating?

But look again:
Try grouping:

- 53 → 50: -3
- 50 → 47: -3
- 47 → 43: -4
- 43 → 40: -3
- 40 → 35: -5
- 35 → 32: -3

Wait — maybe it's alternating between -3 and a decreasing negative? But not clear.

Wait — perhaps this is two interleaved sequences?

Let’s try odd/even positions:

Odd positions (1st, 3rd, 5th, 7th):
53, 47, 40, 32
→ 53 → 47: -6
→ 47 → 40: -7
→ 40 → 32: -8
So next: -9 → 32 - 9 = 23

Even positions (2nd, 4th, 6th):
50, 43, 35
→ 50 → 43: -7
→ 43 → 35: -8
→ Next: -9 → 35 - 9 = 26

But we need to fill in after 32, so the next term is the 8th term (even), which would be 26, then 9th (odd) = 23

Wait — but order is:
1:53, 2:50, 3:47, 4:43, 5:40, 6:35, 7:32, 8:?, 9:?

So 8th term: even → 26
9th term: odd → 23

But let’s confirm:

Odd: 53, 47, 40, 32 → -6, -7, -8 → next -9 → 32 - 9 = 23
Even: 50, 43, 35 → -7, -8 → next -9 → 35 - 9 = 26

So sequence: ..., 32, 26, 23

But wait — the sequence given is:
53, 50, 47, 43, 40, 35, 32, ___, ___

So after 32 (7th term), next is 8th → 26, then 9th → 23

✔ Next two numbers: 26, 23
✔ Rule: Two interleaved sequences:
- Odd positions: decrease by 6, 7, 8, 9...
- Even positions: decrease by 7, 8, 9...

Alternatively: The pattern alternates subtraction with increasing values.

But simpler: It's two sequences:
- First sequence (odd indices): 53, 47, 40, 32, 23 → subtract 6, 7, 8, 9
- Second sequence (even indices): 50, 43, 35, 26 → subtract 7, 8, 9

✔ So answer: 26, 23

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7) 94, 91, 86, 79, 70, 59, 46, ___ , ___

Differences:
- 94 → 91: -3
- 91 → 86: -5
- 86 → 79: -7
- 79 → 70: -9
- 70 → 59: -11
- 59 → 46: -13

So decreasing by odd numbers: -3, -5, -7, -9, -11, -13 → next: -15, -17

So:
- 46 - 15 = 31
- 31 - 17 = 14

✔ Next two numbers: 31, 14
✔ Rule: Subtract consecutive odd numbers: -3, -5, -7, -9, -11, -13, -15, -17...

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8) 63, 67, 64, 68, 65, 69, 66, ___ , ___

Look at the pattern:
- 63 → 67: +4
- 67 → 64: -3
- 64 → 68: +4
- 68 → 65: -3
- 65 → 69: +4
- 69 → 66: -3

So alternating: +4, -3, +4, -3, +4, -3

After 66:
- 66 + 4 = 70
- 70 - 3 = 67

✔ Next two numbers: 70, 67
✔ Rule: Add 4, subtract 3, repeat.

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9) 19, 25, 32, 40, 49, 59, 70, ___ , ___

Differences:
- 19 → 25: +6
- 25 → 32: +7
- 32 → 40: +8
- 40 → 49: +9
- 49 → 59: +10
- 59 → 70: +11

Increasing by 1 each time: +6, +7, +8, +9, +10, +11

So next:
- 70 + 12 = 82
- 82 + 13 = 95

✔ Next two numbers: 82, 95
✔ Rule: Add increasing integers starting from 6: +6, +7, +8, +9, +10, +11, +12, +13...

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10) 29, 31, 34, 38, 43, 49, 56, ___ , ___

Differences:
- 29 → 31: +2
- 31 → 34: +3
- 34 → 38: +4
- 38 → 43: +5
- 43 → 49: +6
- 49 → 56: +7

Increasing by 1 each time: +2, +3, +4, +5, +6, +7

So next:
- 56 + 8 = 64
- 64 + 9 = 73

✔ Next two numbers: 64, 73
✔ Rule: Add increasing integers starting from 2: +2, +3, +4, +5, +6, +7, +8, +9...

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✔ Final Answers:

| # | Sequence | Next Two Numbers | Pattern Rule |
|---|--------|------------------|--------------|
| 1 | 4, 8, 11, 22, 25, 50, 53 | 106, 109 | Multiply by 2, add 3, repeat |
| 2 | 20, 15, 25, 20, 30, 25, 35 | 30, 40 | Subtract 5, add 10, repeat |
| 3 | 48, 57, 65, 72, 78, 83, 87 | 90, 92 | Add 9, 8, 7, 6, 5, 4, 3, 2... |
| 4 | 2, 4, 6, 12, 14, 28, 30 | 60, 62 | Add 2, add 2, multiply by 2, repeat |
| 5 | 3, 6, 5, 10, 9, 18, 17 | 34, 33 | Multiply by 2, subtract 1, repeat |
| 6 | 53, 50, 47, 43, 40, 35, 32 | 26, 23 | Two interleaved sequences: odd pos: -6, -7, -8, -9; even pos: -7, -8, -9 |
| 7 | 94, 91, 86, 79, 70, 59, 46 | 31, 14 | Subtract consecutive odd numbers: -3, -5, -7, -9, -11, -13, -15, -17 |
| 8 | 63, 67, 64, 68, 65, 69, 66 | 70, 67 | Add 4, subtract 3, repeat |
| 9 | 19, 25, 32, 40, 49, 59, 70 | 82, 95 | Add increasing numbers: +6, +7, +8, +9, +10, +11, +12, +13 |
|10 | 29, 31, 34, 38, 43, 49, 56 | 64, 73 | Add increasing numbers: +2, +3, +4, +5, +6, +7, +8, +9 |

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You can now fill in the blanks on the worksheet accordingly!