Let's solve each pattern step by step and write the rule that describes how the numbers change.
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1) 12, 15, 18, 21, 24, 27, 30, 33
- Start at 12.
- Each number increases by 3.
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Rule: Start at 12. Add 3 each time.
✔
*(Already given as an example)*
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2) 45, 40, 35, 30, 25, 20, 15, 10
- Start at 45.
- Each number decreases by 5.
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Rule: Start at 45. Subtract 5 each time.
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3) 6, 8, 10, 12, 14, 16, 18, 20
- Start at 6.
- Each number increases by 2.
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Rule: Start at 6. Add 2 each time.
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4) 20, 30, 40, 50, 60, 70, 80, 90
- Start at 20.
- Each number increases by 10.
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Rule: Start at 20. Add 10 each time.
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5) 56, 49, 42, 35, 28, 21, 14, 7
- Start at 56.
- Each number decreases by 7.
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Rule: Start at 56. Subtract 7 each time.
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6) 11, 22, 33, 44, 55, 66, 77, 88
- Start at 11.
- Each number increases by 11.
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Rule: Start at 11. Add 11 each time.
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7) 81, 72, 63, 54, 45, 36, 27, 18
- Start at 81.
- Each number decreases by 9.
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Rule: Start at 81. Subtract 9 each time.
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8) 15, 19, 23, 27, 31, 35, 39, 43
- Start at 15.
- Each number increases by 4.
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Rule: Start at 15. Add 4 each time.
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9) 65, 62, 59, 56, 53, 50, 47, 44
- Start at 65.
- Each number decreases by 3.
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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.
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These are all
arithmetic sequences, where each term changes by a constant amount (common difference). The rule is usually written as:
"Start at [first number]. [Add/Subtract] [difference] each time."
Parent Tip: Review the logic above to help your child master the concept of number patterns worksheet 5th grade.
