Number patterns worksheet for practicing sequence recognition and arithmetic progression.

Let's solve each of the number pattern problems step by step.

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Problem 1:

Pattern: 104, 113, 122, 131, 140 ...

#### Step 1: Find the difference between consecutive numbers:
- 113 - 104 = 9
- 122 - 113 = 9
- 131 - 122 = 9
- 140 - 131 = 9

✔ The pattern increases by 9 each time.

#### Step 2: Add 9 to find the next three numbers:
- 140 + 9 = 149
- 149 + 9 = 158
- 158 + 9 = 167

✔ Next three numbers: 149, 158, 167

#### Explanation:
The pattern increases by 9 each time. Since the difference is constant, this is an arithmetic sequence with a common difference of 9.

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Problem 2:

Pattern: 331, 316, 301, 286, 271 ...

#### Step 1: Find the difference between consecutive numbers:
- 316 - 331 = -15
- 301 - 316 = -15
- 286 - 301 = -15
- 271 - 286 = -15

✔ The pattern decreases by 15 each time.

#### Step 2: Subtract 15 to find the next three numbers:
- 271 - 15 = 256
- 256 - 15 = 241
- 241 - 15 = 226

✔ Next three numbers: 256, 241, 226

#### Explanation:
This is an arithmetic sequence decreasing by 15 each time.

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Problem 3:

Pattern: 890, 780, 670, 560, 450 ...

#### Step 1: Find the difference between consecutive numbers:
- 780 - 890 = -110
- 670 - 780 = -110
- 560 - 670 = -110
- 450 - 560 = -110

✔ The pattern decreases by 110 each time.

#### Step 2: Subtract 110 to find the next three numbers:
- 450 - 110 = 340
- 340 - 110 = 230
- 230 - 110 = 120

✔ Next three numbers: 340, 230, 120

#### Explanation:
This is another arithmetic sequence decreasing by 110 each time.

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✔ Final Answers:

1.
Next three numbers: 149, 158, 167
How do you know? → The numbers increase by 9 each time.

2.
Next three numbers: 256, 241, 226
How do you know? → The numbers decrease by 15 each time.

3.
Next three numbers: 340, 230, 120
How do you know? → The numbers decrease by 110 each time.

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All patterns are arithmetic sequences with a constant difference. You can identify the rule by subtracting consecutive terms and then applying that rule to extend the pattern.