Worksheets for identifying number pattern rules using addition and subtraction.

Problem Description:

The task involves identifying number patterns and determining whether they follow an addition or subtraction rule. The goal is to complete the missing numbers in each sequence and describe the rule used for each pattern.

Solution:

#### Step 1: Analyze Each Sequence
We will examine each sequence, identify the pattern (addition or subtraction), and fill in the missing numbers.

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#### Sequence 1: 14, 18, 22, ______, ______, ______
- Rule Identification:
- Difference between consecutive terms:
- \( 18 - 14 = 4 \)
- \( 22 - 18 = 4 \)
- The pattern increases by +4.
- Missing Numbers:
- Next term: \( 22 + 4 = 26 \)
- Next term: \( 26 + 4 = 30 \)
- Next term: \( 30 + 4 = 34 \)
- Completed Sequence: \( 14, 18, 22, 26, 30, 34 \)
- Rule: Addition (+4)

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#### Sequence 2: 28, 26, 24, ______, ______, ______
- Rule Identification:
- Difference between consecutive terms:
- \( 26 - 28 = -2 \)
- \( 24 - 26 = -2 \)
- The pattern decreases by -2.
- Missing Numbers:
- Next term: \( 24 - 2 = 22 \)
- Next term: \( 22 - 2 = 20 \)
- Next term: \( 20 - 2 = 18 \)
- Completed Sequence: \( 28, 26, 24, 22, 20, 18 \)
- Rule: Subtraction (-2)

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#### Sequence 3: 65, ______, 75, 80, ______, ______
- Rule Identification:
- Difference between known terms:
- \( 80 - 75 = 5 \)
- Assume the pattern increases by +5.
- Verify: \( 75 - 65 = 10 \) (not consistent with +5).
- Re-evaluate: The pattern might be irregular or involve a different rule.
- Upon closer inspection, the pattern seems to increase by +5 starting from 75.
- Missing Numbers:
- Missing term before 75: \( 65 + 5 = 70 \)
- Next term after 80: \( 80 + 5 = 85 \)
- Next term after 85: \( 85 + 5 = 90 \)
- Completed Sequence: \( 65, 70, 75, 80, 85, 90 \)
- Rule: Addition (+5)

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#### Sequence 4: 150, 145, ______, 135, ______, ______
- Rule Identification:
- Difference between consecutive terms:
- \( 145 - 150 = -5 \)
- Assume the pattern decreases by -5.
- Verify: \( 135 - 145 = -10 \) (not consistent with -5).
- Re-evaluate: The pattern decreases by -5 starting from 145.
- Missing Numbers:
- Missing term: \( 145 - 5 = 140 \)
- Next term: \( 135 - 5 = 130 \)
- Next term: \( 130 - 5 = 125 \)
- Completed Sequence: \( 150, 145, 140, 135, 130, 125 \)
- Rule: Subtraction (-5)

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#### Sequence 5: 36, 30, 24, ______, ______, ______
- Rule Identification:
- Difference between consecutive terms:
- \( 30 - 36 = -6 \)
- \( 24 - 30 = -6 \)
- The pattern decreases by -6.
- Missing Numbers:
- Next term: \( 24 - 6 = 18 \)
- Next term: \( 18 - 6 = 12 \)
- Next term: \( 12 - 6 = 6 \)
- Completed Sequence: \( 36, 30, 24, 18, 12, 6 \)
- Rule: Subtraction (-6)

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#### Sequence 6: 90, ______, 96, 99, ______, ______
- Rule Identification:
- Difference between known terms:
- \( 96 - 90 = 6 \)
- \( 99 - 96 = 3 \)
- The pattern alternates between +6 and +3.
- Missing Numbers:
- Missing term: \( 90 + 6 = 96 \) (already given, so next term is \( 96 + 3 = 99 \)).
- Next term: \( 99 + 6 = 105 \)
- Next term: \( 105 + 3 = 108 \)
- Completed Sequence: \( 90, 96, 96, 99, 105, 108 \)
- Rule: Alternating Addition (+6, +3)

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#### Sequence 7: 201, 211, 221, ______, ______, ______
- Rule Identification:
- Difference between consecutive terms:
- \( 211 - 201 = 10 \)
- \( 221 - 211 = 10 \)
- The pattern increases by +10.
- Missing Numbers:
- Next term: \( 221 + 10 = 231 \)
- Next term: \( 231 + 10 = 241 \)
- Next term: \( 241 + 10 = 251 \)
- Completed Sequence: \( 201, 211, 221, 231, 241, 251 \)
- Rule: Addition (+10)

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#### Sequence 8: 77, 66, 55, ______, ______, ______
- Rule Identification:
- Difference between consecutive terms:
- \( 66 - 77 = -11 \)
- \( 55 - 66 = -11 \)
- The pattern decreases by -11.
- Missing Numbers:
- Next term: \( 55 - 11 = 44 \)
- Next term: \( 44 - 11 = 33 \)
- Next term: \( 33 - 11 = 22 \)
- Completed Sequence: \( 77, 66, 55, 44, 33, 22 \)
- Rule: Subtraction (-11)

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Final Answer:

\[
\boxed{
\begin{aligned}
&\text{Sequence 1: } 14, 18, 22, 26, 30, 34 \quad \text{(Addition +4)} \\
&\text{Sequence 2: } 28, 26, 24, 22, 20, 18 \quad \text{(Subtraction -2)} \\
&\text{Sequence 3: } 65, 70, 75, 80, 85, 90 \quad \text{(Addition +5)} \\
&\text{Sequence 4: } 150, 145, 140, 135, 130, 125 \quad \text{(Subtraction -5)} \\
&\text{Sequence 5: } 36, 30, 24, 18, 12, 6 \quad \text{(Subtraction -6)} \\
&\text{Sequence 6: } 90, 96, 96, 99, 105, 108 \quad \text{(Alternating +6, +3)} \\
&\text{Sequence 7: } 201, 211, 221, 231, 241, 251 \quad \text{(Addition +10)} \\
&\text{Sequence 8: } 77, 66, 55, 44, 33, 22 \quad \text{(Subtraction -11)}
\end{aligned}
}
\]