Pattern Worksheets - Free Printable

Let's solve each pattern step by step and write the rule that describes each sequence.

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1) 12, 15, 18, 21, 24, 27, 30, 33

- Start at 12.
- Add 3 each time:
12 → 15 (12 + 3), 15 → 18 (15 + 3), etc.
- Rule: Start at 12. Add 3 each time. ✔

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2) 45, 40, 35, 30, 25, 20, 15, 10

- Start at 45.
- Subtract 5 each time:
45 → 40 (45 - 5), 40 → 35 (40 - 5), etc.
- Rule: Start at 45. Subtract 5 each time.

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3) 6, 8, 10, 12, 14, 16, 18, 20

- Start at 6.
- Add 2 each time:
6 → 8 (6 + 2), 8 → 10 (8 + 2), etc.
- Rule: Start at 6. Add 2 each time.

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4) 20, 30, 40, 50, 60, 70, 80, 90

- Start at 20.
- Add 10 each time:
20 → 30 (20 + 10), 30 → 40 (30 + 10), etc.
- Rule: Start at 20. Add 10 each time.

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5) 56, 49, 42, 35, 28, 21, 14, 7

- Start at 56.
- Subtract 7 each time:
56 → 49 (56 - 7), 49 → 42 (49 - 7), etc.
- Rule: Start at 56. Subtract 7 each time.

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6) 11, 22, 33, 44, 55, 66, 77, 88

- Start at 11.
- Add 11 each time:
11 → 22 (11 + 11), 22 → 33 (22 + 11), etc.
- Rule: Start at 11. Add 11 each time.

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7) 81, 72, 63, 54, 45, 36, 27, 18

- Start at 81.
- Subtract 9 each time:
81 → 72 (81 - 9), 72 → 63 (72 - 9), etc.
- Rule: Start at 81. Subtract 9 each time.

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8) 15, 19, 23, 27, 31, 35, 39, 43

- Start at 15.
- Add 4 each time:
15 → 19 (15 + 4), 19 → 23 (19 + 4), etc.
- Rule: Start at 15. Add 4 each time.

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9) 65, 62, 59, 56, 53, 50, 47, 44

- Start at 65.
- Subtract 3 each time:
65 → 62 (65 - 3), 62 → 59 (62 - 3), etc.
- Rule: Start at 65. Subtract 3 each time.

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Final Answers:

1) Start at 12. Add 3 each time.
2) Start at 45. Subtract 5 each time.
3) Start at 6. Add 2 each time.
4) Start at 20. Add 10 each time.
5) Start at 56. Subtract 7 each time.
6) Start at 11. Add 11 each time.
7) Start at 81. Subtract 9 each time.
8) Start at 15. Add 4 each time.
9) Start at 65. Subtract 3 each time.

✔ All patterns follow a simple arithmetic sequence (either adding or subtracting a constant).