Math worksheet for practicing number patterns with a fun detective theme.

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 alternates between two different patterns:
1. Adding 7: \( 8 + 7 = 15 \), \( 15 + 9 = 24 \), \( 24 + 9 = 33 \)
2. Adding 2: \( 15 + 1 = 16 \) (but it's given as 26, so we adjust), \( 24 + 2 = 26 \), \( 33 + 2 = 35 \)

- Next numbers:
- Continue the pattern of adding 7: \( 35 + 7 = 42 \)
- Then add 2: \( 42 + 2 = 44 \)
- Then add 7 again: \( 44 + 7 = 51 \)

- Answer: 42, 44, 51

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

- Next numbers:
- \( 17 - 2 = 15 \)
- \( 15 - 2 = 13 \)
- \( 13 - 2 = 11 \)

- Answer: 15, 13, 11

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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...

- Next numbers:
- \( 24 \times 2 = 48 \)
- \( 96 \times 2 = 192 \) (already given)
- \( 192 \times 2 = 384 \)
- \( 384 \times 2 = 768 \)

- 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.
- \( 0^2 = 0 \)
- \( 1^2 = 1 \)
- \( 2^2 = 4 \)
- \( 3^2 = 9 \)
- \( 4^2 = 16 \)
- And so on...

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

- Answer: The secret pattern is that each number is a perfect square of an integer.

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Final Answers:

1. 28, 31
2. 48, 53, 63
3. 42, 44, 51
4. 15, 13, 11
5. 48, 384, 768
Bonus: The sequence is the squares of consecutive integers: \( n^2 \).

Boxed Answers:
\[
\boxed{28, 31; 48, 53, 63; 42, 44, 51; 15, 13, 11; 48, 384, 768}
\]