Number Patterns worksheet for practicing sequence recognition and pattern extension.

Problem Overview:

The task involves extending number patterns and stating the rule for each sequence. The goal is to identify the pattern in each sequence, determine the next two numbers, and describe the rule.

Solution:

#### 1) Sequence: 21, 27, 33, 39, 45, 51, 57, ______, ______
- Pattern Analysis: Each number increases by 6.
- \( 27 - 21 = 6 \)
- \( 33 - 27 = 6 \)
- \( 39 - 33 = 6 \)
- And so on.
- Next Two Numbers:
- \( 57 + 6 = 63 \)
- \( 63 + 6 = 69 \)
- Rule: Add 6 to each term.
- Answer: 63, 69

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#### 2) Sequence: 69, 64, 59, 54, 49, 44, 39, ______, ______
- Pattern Analysis: Each number decreases by 5.
- \( 64 - 69 = -5 \)
- \( 59 - 64 = -5 \)
- \( 54 - 59 = -5 \)
- And so on.
- Next Two Numbers:
- \( 39 - 5 = 34 \)
- \( 34 - 5 = 29 \)
- Rule: Subtract 5 from each term.
- Answer: 34, 29

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#### 3) Sequence: 79, 70, 61, 52, 43, 34, 25, ______, ______
- Pattern Analysis: Each number decreases by 9.
- \( 70 - 79 = -9 \)
- \( 61 - 70 = -9 \)
- \( 52 - 61 = -9 \)
- And so on.
- Next Two Numbers:
- \( 25 - 9 = 16 \)
- \( 16 - 9 = 7 \)
- Rule: Subtract 9 from each term.
- Answer: 16, 7

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#### 4) Sequence: 83, 74, 65, 56, 47, 38, 29, ______, ______
- Pattern Analysis: Each number decreases by 9.
- \( 74 - 83 = -9 \)
- \( 65 - 74 = -9 \)
- \( 56 - 65 = -9 \)
- And so on.
- Next Two Numbers:
- \( 29 - 9 = 20 \)
- \( 20 - 9 = 11 \)
- Rule: Subtract 9 from each term.
- Answer: 20, 11

---

#### 5) Sequence: 77, 70, 63, 56, 49, 42, 35, ______, ______
- Pattern Analysis: Each number decreases by 7.
- \( 70 - 77 = -7 \)
- \( 63 - 70 = -7 \)
- \( 56 - 63 = -7 \)
- And so on.
- Next Two Numbers:
- \( 35 - 7 = 28 \)
- \( 28 - 7 = 21 \)
- Rule: Subtract 7 from each term.
- Answer: 28, 21

---

#### 6) Sequence: 30, 35, 40, 45, 50, 55, 60, ______, ______
- Pattern Analysis: Each number increases by 5.
- \( 35 - 30 = 5 \)
- \( 40 - 35 = 5 \)
- \( 45 - 40 = 5 \)
- And so on.
- Next Two Numbers:
- \( 60 + 5 = 65 \)
- \( 65 + 5 = 70 \)
- Rule: Add 5 to each term.
- Answer: 65, 70

---

#### 7) Sequence: 44, 46, 48, 50, 52, 54, 56, ______, ______
- Pattern Analysis: Each number increases by 2.
- \( 46 - 44 = 2 \)
- \( 48 - 46 = 2 \)
- \( 50 - 48 = 2 \)
- And so on.
- Next Two Numbers:
- \( 56 + 2 = 58 \)
- \( 58 + 2 = 60 \)
- Rule: Add 2 to each term.
- Answer: 58, 60

---

#### 8) Sequence: 85, 78, 71, 64, 57, 50, 43, ______, ______
- Pattern Analysis: Each number decreases by 7.
- \( 78 - 85 = -7 \)
- \( 71 - 78 = -7 \)
- \( 64 - 71 = -7 \)
- And so on.
- Next Two Numbers:
- \( 43 - 7 = 36 \)
- \( 36 - 7 = 29 \)
- Rule: Subtract 7 from each term.
- Answer: 36, 29

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#### 9) Sequence: 20, 26, 32, 38, 44, 50, 56, ______, ______
- Pattern Analysis: Each number increases by 6.
- \( 26 - 20 = 6 \)
- \( 32 - 26 = 6 \)
- \( 38 - 32 = 6 \)
- And so on.
- Next Two Numbers:
- \( 56 + 6 = 62 \)
- \( 62 + 6 = 68 \)
- Rule: Add 6 to each term.
- Answer: 62, 68

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#### 10) Sequence: 64, 61, 58, 55, 52, 49, 46, ______, ______
- Pattern Analysis: Each number decreases by 3.
- \( 61 - 64 = -3 \)
- \( 58 - 61 = -3 \)
- \( 55 - 58 = -3 \)
- And so on.
- Next Two Numbers:
- \( 46 - 3 = 43 \)
- \( 43 - 3 = 40 \)
- Rule: Subtract 3 from each term.
- Answer: 43, 40

---

Final Answers:

1. 63, 69
2. 34, 29
3. 16, 7
4. 20, 11
5. 28, 21
6. 65, 70
7. 58, 60
8. 36, 29
9. 62, 68
10. 43, 40

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. 63, 69 \\
2. 34, 29 \\
3. 16, 7 \\
4. 20, 11 \\
5. 28, 21 \\
6. 65, 70 \\
7. 58, 60 \\
8. 36, 29 \\
9. 62, 68 \\
10. 43, 40 \\
\end{array}
}
\]