Problem Analysis:
The task involves identifying patterns in sequences of numbers and determining the next number in each sequence. Additionally, we need to write the rule that governs each sequence.
---
Step-by-Step Solution:
####
Part 1: Write the next number in the sequence. Then, write what the pattern is for that sequence.
1.
Sequence: 2, 4, 6, 8, 10, 12, ______
-
Pattern: The numbers increase by 2 each time.
-
Next Number: \( 12 + 2 = 14 \)
-
Rule: Add 2
-
Answer: 14, Rule: Add 2
2.
Sequence: 3, 6, 9, 12, 15, 18, ______
-
Pattern: The numbers increase by 3 each time.
-
Next Number: \( 18 + 3 = 21 \)
-
Rule: Add 3
-
Answer: 21, Rule: Add 3
3.
Sequence: 23, 20, 17, 14, 11, 8, ______
-
Pattern: The numbers decrease by 3 each time.
-
Next Number: \( 8 - 3 = 5 \)
-
Rule: Subtract 3
-
Answer: 5, Rule: Subtract 3
4.
Sequence: 4, 14, 24, 34, 44, 54, ______
-
Pattern: The numbers increase by 10 each time.
-
Next Number: \( 54 + 10 = 64 \)
-
Rule: Add 10
-
Answer: 64, Rule: Add 10
5.
Sequence: 52, 44, 36, 28, 20, 12, ______
-
Pattern: The numbers decrease by 8 each time.
-
Next Number: \( 12 - 8 = 4 \)
-
Rule: Subtract 8
-
Answer: 4, Rule: Subtract 8
6.
Sequence: 7, 14, 21, 28, 35, 42, ______
-
Pattern: The numbers increase by 7 each time.
-
Next Number: \( 42 + 7 = 49 \)
-
Rule: Add 7
-
Answer: 49, Rule: Add 7
---
####
Part 2: Write the next number in each sequence according to the rule.
1.
Rule: Add 5
- Sequence: 55, 60, 65, ______, ______, ______
-
Pattern: Each number increases by 5.
- Next Numbers:
- \( 65 + 5 = 70 \)
- \( 70 + 5 = 75 \)
- \( 75 + 5 = 80 \)
-
Answer: 70, 75, 80
2.
Rule: Subtract 11
- Sequence: 88, 77, ______, ______, ______
-
Pattern: Each number decreases by 11.
- Next Numbers:
- \( 77 - 11 = 66 \)
- \( 66 - 11 = 55 \)
- \( 55 - 11 = 44 \)
-
Answer: 66, 55, 44
3.
Rule: Add 9
- Sequence: 0, ______, ______, ______
-
Pattern: Each number increases by 9.
- Next Numbers:
- \( 0 + 9 = 9 \)
- \( 9 + 9 = 18 \)
- \( 18 + 9 = 27 \)
-
Answer: 9, 18, 27
---
Final Answers:
1.
14, Rule: Add 2
2.
21, Rule: Add 3
3.
5, Rule: Subtract 3
4.
64, Rule: Add 10
5.
4, Rule: Subtract 8
6.
49, Rule: Add 7
7.
70, 75, 80
8.
66, 55, 44
9.
9, 18, 27
Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \text{14, Rule: Add 2} \\
2. \text{21, Rule: Add 3} \\
3. \text{5, Rule: Subtract 3} \\
4. \text{64, Rule: Add 10} \\
5. \text{4, Rule: Subtract 8} \\
6. \text{49, Rule: Add 7} \\
7. \text{70, 75, 80} \\
8. \text{66, 55, 44} \\
9. \text{9, 18, 27}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of pattern rule worksheet grade 7.
