Math worksheet for identifying and completing number patterns.

Problem: Solve the number patterns and explain the solution.

#### 1. Sequence: 1, 4, 7, 10, 13, 16, 19, 22, 25, ____, ____
- Pattern: The sequence increases by 3 each time.
- \( 1 + 3 = 4 \)
- \( 4 + 3 = 7 \)
- \( 7 + 3 = 10 \)
- And so on...

- Next numbers:
- \( 25 + 3 = 28 \)
- \( 28 + 3 = 31 \)

- Answer: 28, 31

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#### 2. Sequence: 3, 8, 13, 18, 23, 33, 38, ____, ____, ____
- Pattern: The sequence alternates between adding 5 and adding 10.
- \( 3 + 5 = 8 \)
- \( 8 + 5 = 13 \)
- \( 13 + 5 = 18 \)
- \( 18 + 5 = 23 \)
- \( 23 + 10 = 33 \)
- \( 33 + 5 = 38 \)

- Next numbers:
- \( 38 + 10 = 48 \)
- \( 48 + 5 = 53 \)
- \( 53 + 10 = 63 \)

- Answer: 48, 53, 63

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#### 3. Sequence: 8, 15, 24, 26, 33, 35, ____, ____, ____
- Pattern: This sequence is a bit tricky because it combines two interleaved patterns:
1. Odd-indexed terms: \( 8, 24, 33, \ldots \) (increasing by 16, then 9)
2. Even-indexed terms: \( 15, 26, 35, \ldots \) (increasing by 11, then 9)

- Odd-indexed terms:
- \( 8 + 16 = 24 \)
- \( 24 + 9 = 33 \)
- Next: \( 33 + 16 = 49 \)

- Even-indexed terms:
- \( 15 + 11 = 26 \)
- \( 26 + 9 = 35 \)
- Next: \( 35 + 11 = 46 \)

- Combining the next three terms:
- Next odd-indexed term: 49
- Next even-indexed term: 46
- Next odd-indexed term: \( 49 + 9 = 58 \)

- Answer: 49, 46, 58

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#### 4. Sequence: 25, 23, 21, 19, 17, 15, ____, ____, ____
- Pattern: The sequence decreases by 2 each time.
- \( 25 - 2 = 23 \)
- \( 23 - 2 = 21 \)
- And so on...

- Next numbers:
- \( 15 - 2 = 13 \)
- \( 13 - 2 = 11 \)
- \( 11 - 2 = 9 \)

- Answer: 13, 11, 9

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#### 5. Sequence: 3, 6, 12, 24, ____, 96, 192, ____, ____
- Pattern: Each term is multiplied by 2 to get the next term.
- \( 3 \times 2 = 6 \)
- \( 6 \times 2 = 12 \)
- \( 12 \times 2 = 24 \)
- And so on...

- Missing terms:
- \( 24 \times 2 = 48 \)
- \( 192 \times 2 = 384 \)
- \( 384 \times 2 = 768 \)

- Answer: 48, 384, 768

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#### Bonus: Sequence: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81
- Pattern: These are perfect squares of consecutive integers.
- \( 0^2 = 0 \)
- \( 1^2 = 1 \)
- \( 2^2 = 4 \)
- \( 3^2 = 9 \)
- And so on...

- Explanation: The sequence represents \( n^2 \) for \( n = 0, 1, 2, 3, \ldots \).

- Answer: The secret pattern is "perfect squares."

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Final Answers:

1. 28, 31
2. 48, 53, 63
3. 49, 46, 58
4. 13, 11, 9
5. 48, 384, 768
Bonus: Perfect squares

\boxed{28, 31; 48, 53, 63; 49, 46, 58; 13, 11, 9; 48, 384, 768}