Sequence & Number Patterns Worksheets | PrintablEducation - Free Printable

Let's solve each sequence step by step and identify the pattern.

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1. 17, 20, 23, 26, __, __, __

- Differences:
20 - 17 = 3
23 - 20 = 3
26 - 23 = 3
→ Adding 3 each time.

Next numbers:
26 + 3 = 29
29 + 3 = 32
32 + 3 = 35

✔ Answer: 29, 32, 35
✔ Pattern: Add 3 each time (arithmetic sequence with common difference 3)

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2. 34, 32, 30, 28, __, __, __

- Differences:
32 - 34 = -2
30 - 32 = -2
28 - 30 = -2
→ Subtracting 2 each time.

Next numbers:
28 - 2 = 26
26 - 2 = 24
24 - 2 = 22

✔ Answer: 26, 24, 22
✔ Pattern: Subtract 2 each time (arithmetic sequence with common difference -2)

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3. 17, 21, 25, 29, __, __, __

- Differences:
21 - 17 = 4
25 - 21 = 4
29 - 25 = 4
→ Add 4 each time.

Next numbers:
29 + 4 = 33
33 + 4 = 37
37 + 4 = 41

✔ Answer: 33, 37, 41
✔ Pattern: Add 4 each time

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4. 80, 75, 70, 65, __, __, __

- Differences:
75 - 80 = -5
70 - 75 = -5
65 - 70 = -5
→ Subtract 5 each time.

Next numbers:
65 - 5 = 60
60 - 5 = 55
55 - 5 = 50

✔ Answer: 60, 55, 50
✔ Pattern: Subtract 5 each time

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5. 12, 18, 24, 30, __, __, __

- Differences:
18 - 12 = 6
24 - 18 = 6
30 - 24 = 6
→ Add 6 each time.

Next numbers:
30 + 6 = 36
36 + 6 = 42
42 + 6 = 48

✔ Answer: 36, 42, 48
✔ Pattern: Add 6 each time

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6. 87, 81, 75, 69, __, __, __

- Differences:
81 - 87 = -6
75 - 81 = -6
69 - 75 = -6
→ Subtract 6 each time.

Next numbers:
69 - 6 = 63
63 - 6 = 57
57 - 6 = 51

✔ Answer: 63, 57, 51
✔ Pattern: Subtract 6 each time

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7. 18, 20, 22, 24, __, __, __

- Differences:
20 - 18 = 2
22 - 20 = 2
24 - 22 = 2
→ Add 2 each time.

Next numbers:
24 + 2 = 26
26 + 2 = 28
28 + 2 = 30

✔ Answer: 26, 28, 30
✔ Pattern: Add 2 each time

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8. 12, 15, 18, 21, __, __, __

- Differences:
15 - 12 = 3
18 - 15 = 3
21 - 18 = 3
→ Add 3 each time.

Next numbers:
21 + 3 = 24
24 + 3 = 27
27 + 3 = 30

✔ Answer: 24, 27, 30
✔ Pattern: Add 3 each time

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9. 32, 30, 28, 26, __, __, __

- Differences:
30 - 32 = -2
28 - 30 = -2
26 - 28 = -2
→ Subtract 2 each time.

Next numbers:
26 - 2 = 24
24 - 2 = 22
22 - 2 = 20

✔ Answer: 24, 22, 20
✔ Pattern: Subtract 2 each time

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10. 29, 34, 39, 44, __, __, __

- Differences:
34 - 29 = 5
39 - 34 = 5
44 - 39 = 5
→ Add 5 each time.

Next numbers:
44 + 5 = 49
49 + 5 = 54
54 + 5 = 59

✔ Answer: 49, 54, 59
✔ Pattern: Add 5 each time

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11. 21, 25, 29, 33, __, __, __

- Differences:
25 - 21 = 4
29 - 25 = 4
33 - 29 = 4
→ Add 4 each time.

Next numbers:
33 + 4 = 37
37 + 4 = 41
41 + 4 = 45

✔ Answer: 37, 41, 45
✔ Pattern: Add 4 each time

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12. 88, 81, 74, 67, __, __, __

- Differences:
81 - 88 = -7
74 - 81 = -7
67 - 74 = -7
→ Subtract 7 each time.

Next numbers:
67 - 7 = 60
60 - 7 = 53
53 - 7 = 46

✔ Answer: 60, 53, 46
✔ Pattern: Subtract 7 each time

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✔ Final Answers:

| Sequence | Completed | Pattern |
|--------|-----------|---------|
| 17, 20, 23, 26 | 29, 32, 35 | Add 3 |
| 34, 32, 30, 28 | 26, 24, 22 | Subtract 2 |
| 17, 21, 25, 29 | 33, 37, 41 | Add 4 |
| 80, 75, 70, 65 | 60, 55, 50 | Subtract 5 |
| 12, 18, 24, 30 | 36, 42, 48 | Add 6 |
| 87, 81, 75, 69 | 63, 57, 51 | Subtract 6 |
| 18, 20, 22, 24 | 26, 28, 30 | Add 2 |
| 12, 15, 18, 21 | 24, 27, 30 | Add 3 |
| 32, 30, 28, 26 | 24, 22, 20 | Subtract 2 |
| 29, 34, 39, 44 | 49, 54, 59 | Add 5 |
| 21, 25, 29, 33 | 37, 41, 45 | Add 4 |
| 88, 81, 74, 67 | 60, 53, 46 | Subtract 7 |

All sequences follow arithmetic patterns, where a constant number is added or subtracted to get the next term.

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