Pattern Worksheets - Free Pattern Recognition Worksheets - Free Printable

Let's solve each number pattern step by step. We are given a series of number lines with missing numbers, and we need to determine the rule (pattern) for each sequence and fill in the blanks.

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1. First Line: 72, __, 68

- Numbers: 72, ?, 68
- The pattern appears to be decreasing.
- From 72 to 68 is a drop of 4 over two steps → so decrease by 2 each time.
- So: 72 → 70 → 68

✔ Answer: 70

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2. Second Line: 116, 120, 124

- Numbers: 116, 120, 124
- Pattern: +4 each time
- So next numbers: 128, 132, 136, 140, etc.
- But the line has more boxes — let’s count:
- We have 116, 120, 124 → that’s three numbers
- Then there are several empty boxes after

So the pattern is +4.

- After 124: 128, 132, 136, 140, 144, 148, 152, 156, 160

But since the number line only shows up to 160? Let's see how many boxes.

Wait — actually, looking at the image description, it seems like each line has about 10–12 tick marks. Let's assume the pattern continues every 4 units.

So:
- 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160

✔ Missing numbers: 128, 132, 136, 140, 144, 148, 152, 156, 160

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3. Third Line: 75, 85, 95

- Numbers: 75, 85, 95 → increasing by 10
- Next numbers: 105, 115, 125, 135, 145, 155, 165, 175, 185

✔ Pattern: +10

So fill in: 105, 115, 125, 135, 145, 155, 165, 175, 185

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4. Fourth Line: 58, 55, 52, 49

- Numbers: 58, 55, 52, 49 → decreasing by 3
- Next: 46, 43, 40, 37, 34, 31, 28, 25, 22, 19, 16

✔ Pattern: –3

So continue: 46, 43, 40, 37, 34, 31, 28, 25, 22, 19, 16

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5. Fifth Line: 1, 2, 5, 10, 17

- Numbers: 1, 2, 5, 10, 17
- Look at differences:
- 2 – 1 = 1
- 5 – 2 = 3
- 10 – 5 = 5
- 17 – 10 = 7

Differences: +1, +3, +5, +7 → odd numbers increasing by 2

So next difference: +9 → 17 + 9 = 26
Then +11 → 26 + 11 = 37
Then +13 → 37 + 13 = 50
Then +15 → 50 + 15 = 65
Then +17 → 65 + 17 = 82

So sequence: 1, 2, 5, 10, 17, 26, 37, 50, 65, 82

✔ Pattern: Add consecutive odd numbers starting from 1

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6. Sixth Line: 7, 11, 16, 22

- Differences:
- 11 – 7 = 4
- 16 – 11 = 5
- 22 – 16 = 6

So differences: +4, +5, +6 → increasing by 1 each time

Next: +7 → 22 + 7 = 29
Then +8 → 29 + 8 = 37
Then +9 → 37 + 9 = 46
Then +10 → 46 + 10 = 56
Then +11 → 56 + 11 = 67
Then +12 → 67 + 12 = 79

Sequence: 7, 11, 16, 22, 29, 37, 46, 56, 67, 79

✔ Pattern: Add increasing integers: +4, +5, +6, +7, ...

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7. Seventh Line: 2, 3, 5, 8, 12

- Differences:
- 3 – 2 = 1
- 5 – 3 = 2
- 8 – 5 = 3
- 12 – 8 = 4

So differences: +1, +2, +3, +4 → increasing by 1

Next: +5 → 12 + 5 = 17
Then +6 → 17 + 6 = 23
Then +7 → 23 + 7 = 30
Then +8 → 30 + 8 = 38
Then +9 → 38 + 9 = 47

Sequence: 2, 3, 5, 8, 12, 17, 23, 30, 38, 47

✔ Pattern: Add consecutive integers starting from 1

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8. Eighth Line: 2, 4, 8, 16, 32

- This is clearly doubling each time:
- 2 × 2 = 4
- 4 × 2 = 8
- 8 × 2 = 16
- 16 × 2 = 32

Next: 32 × 2 = 64
Then 128, 256, 512, 1024, etc.

So sequence: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024

✔ Pattern: Multiply by 2 each time (powers of 2)

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✔ Final Answers:

Let’s write them out clearly:

1. 72, 70, 68
2. 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160
3. 75, 85, 95, 105, 115, 125, 135, 145, 155, 165, 175, 185
4. 58, 55, 52, 49, 46, 43, 40, 37, 34, 31, 28, 25, 22, 19, 16
5. 1, 2, 5, 10, 17, 26, 37, 50, 65, 82
6. 7, 11, 16, 22, 29, 37, 46, 56, 67, 79
7. 2, 3, 5, 8, 12, 17, 23, 30, 38, 47
8. 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024

> Note: The number of boxes on each line may vary, but the patterns continue as shown above.

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Summary of Patterns:

| Line | Pattern Rule |
|------|--------------|
| 1 | Subtract 2 |
| 2 | Add 4 |
| 3 | Add 10 |
| 4 | Subtract 3 |
| 5 | Add 1, 3, 5, 7, 9... (odd numbers) |
| 6 | Add 4, 5, 6, 7... (increasing by 1) |
| 7 | Add 1, 2, 3, 4... (consecutive integers) |
| 8 | Multiply by 2 |

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