Patterns & Function Machine Worksheets | Free - Distance Learning ... - Free Printable

Let's solve each pattern step by step and find the next number in each sequence. We'll analyze the rule behind each pattern.

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1) 8, 40, 200, ______

Look at the pattern:

- 8 → 40:
$ 8 \times 5 = 40 $
- 40 → 200:
$ 40 \times 5 = 200 $

So, multiply by 5 each time.

→ Next: $ 200 \times 5 = \boxed{1000} $

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2) 2, 6, 10, 14, 18, ______

Check differences:

- 6 - 2 = 4
- 10 - 6 = 4
- 14 - 10 = 4
- 18 - 14 = 4

Add 4 each time.

→ Next: $ 18 + 4 = \boxed{22} $

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3) 40, 20, 10, ______

- 40 → 20: divide by 2
- 20 → 10: divide by 2

So, divide by 2 each time.

→ Next: $ 10 \div 2 = \boxed{5} $

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4) 47, 37, 27, 17, ______

Differences:

- 47 - 37 = 10
- 37 - 27 = 10
- 27 - 17 = 10

Subtract 10 each time.

→ Next: $ 17 - 10 = \boxed{7} $

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5) 26, 22, 18, 14, ______

Differences:

- 26 - 22 = 4
- 22 - 18 = 4
- 18 - 14 = 4

Subtract 4 each time.

→ Next: $ 14 - 4 = \boxed{10} $

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6) 45, 39, 33, 27, 21, 15, ______

Differences:

- 45 - 39 = 6
- 39 - 33 = 6
- 33 - 27 = 6
- 27 - 21 = 6
- 21 - 15 = 6

Subtract 6 each time.

→ Next: $ 15 - 6 = \boxed{9} $

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7) 486, 162, 54, 18, ______

Look at division:

- 486 ÷ 3 = 162
- 162 ÷ 3 = 54
- 54 ÷ 3 = 18

Divide by 3 each time.

→ Next: $ 18 \div 3 = \boxed{6} $

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8) 6, 14, 22, 30, 38, 46, 54, ______

Differences:

- 14 - 6 = 8
- 22 - 14 = 8
- 30 - 22 = 8
- 38 - 30 = 8
- 46 - 38 = 8
- 54 - 46 = 8

Add 8 each time.

→ Next: $ 54 + 8 = \boxed{62} $

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9) 500, 100, 20, ______

Look at ratios:

- 500 → 100: $ 500 \div 5 = 100 $
- 100 → 20: $ 100 \div 5 = 20 $

Divide by 5 each time.

→ Next: $ 20 \div 5 = \boxed{4} $

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10) 4, 20, 100, ______

Check multiplication:

- 4 → 20: $ 4 \times 5 = 20 $
- 20 → 100: $ 20 \times 5 = 100 $

Multiply by 5 each time.

→ Next: $ 100 \times 5 = \boxed{500} $

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11) 9, 45, 225, ______

- 9 → 45: $ 9 \times 5 = 45 $
- 45 → 225: $ 45 \times 5 = 225 $

Multiply by 5.

→ Next: $ 225 \times 5 = \boxed{1125} $

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12) 1, 4, 7, 10, 13, 16, ______

Differences:

- 4 - 1 = 3
- 7 - 4 = 3
- 10 - 7 = 3
- 13 - 10 = 3
- 16 - 13 = 3

Add 3 each time.

→ Next: $ 16 + 3 = \boxed{19} $

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13) 52, 44, 36, 28, 20, 12, ______

Differences:

- 52 - 44 = 8
- 44 - 36 = 8
- 36 - 28 = 8
- 28 - 20 = 8
- 20 - 12 = 8

Subtract 8 each time.

→ Next: $ 12 - 8 = \boxed{4} $

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14) 7, 28, 112, ______

Check multiplication:

- 7 → 28: $ 7 \times 4 = 28 $
- 28 → 112: $ 28 \times 4 = 112 $

Multiply by 4.

→ Next: $ 112 \times 4 = \boxed{448} $

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15) 5, 8, 11, 14, 17, 20, 23, ______

Differences:

- 8 - 5 = 3
- 11 - 8 = 3
- 14 - 11 = 3
- 17 - 14 = 3
- 20 - 17 = 3
- 23 - 20 = 3

Add 3 each time.

→ Next: $ 23 + 3 = \boxed{26} $

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✔ Final Answers:

1. 1000
2. 22
3. 5
4. 7
5. 10
6. 9
7. 6
8. 62
9. 4
10. 500
11. 1125
12. 19
13. 4
14. 448
15. 26

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You can now fill these into the answer column on the worksheet! Let me know if you'd like a printable version or explanation for any specific one.