Lesson 11.2: Geometric Patterns and Multiplicative Rules
Applied concepts and practical problem solving for Geometric Patterns and Multiplicative Rules.
⏱️ Reading Time: 20 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Patterns and Sequences
Computer Code Simulation: Generating fractal branching trees on screen.
💡 Core Mathematical Concepts: Geometric Patterns and Multiplicative Rules
Focus areas: Patterns that double, triple, or alternate mathematical operations..
| Concept / Term | Mathematical Meaning | Real-Life Application |
|---|---|---|
| Multiplicative Sequence | Each term is multiplied by a fixed factor | 3, 6, 12, 24, 48... (rule: ×2) |
| Alternating Sequence | A sequence that alternates between two operations | Add 5, subtract 2, add 5, subtract 2... |
| Square Number Pattern | 1, 4, 9, 16, 25, 36... (1×1, 2×2, 3×3, 4×4...) | Everyday applications |
📝 Step-by-Step Worked Examples
Worked Example 1: Find missing term
2, 6, 18, 54, ? -> Multiplying by 3 -> 54 × 3 = 162.
Worked Example 2: Square numbers
What is the 7th square number? 7 × 7 = 49.
⚠️ Common Misconceptions to Avoid
Common Misconception: Adding instead of multiplying
Correction: Seeing 2, 4, 8 and guessing 10 (+2) instead of 16 (×2).
Common Misconception: Miscounting pattern positions
Correction: Double check term index starting from term 1.
🎯
Self-Check Challenge
A bacteria culture doubles in size every hour. If there are 25 bacteria at the start, how many will there be after 4 hours?
Answer & Explanation:
Hour 1: 50. Hour 2: 100. Hour 3: 200. Hour 4: 400 bacteria.
🎯 Key Learning Takeaways
Extend understanding of Geometric Patterns and Multiplicative Rules.
Solve multi-step real-world problems systematically.
Verify solutions through mathematical reasoning.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G5-M-CH11-WS05
A4 • 15 Qs
Patterns and Sequences: Worksheet 5
Practice Assessment 5 • Central Botanical Gardens Context
G5-M-CH11-WS04
A4 • 15 Qs
Patterns and Sequences: Worksheet 4
Practice Assessment 4 • Eco-Friendly Solar Park Context
G5-M-CH11-WS03
A4 • 15 Qs
Patterns and Sequences: Worksheet 3
Practice Assessment 3 • Harbor Marine Terminal Context
G5-M-CH11-WS02
A4 • 15 Qs
Patterns and Sequences: Worksheet 2
Practice Assessment 2 • Science & Discovery Museum Context
G5-M-CH11-WS01
A4 • 15 Qs
Patterns and Sequences: Worksheet 1
Practice Assessment 1 • City Regional Airport Context
✍️ Lesson Practice Questions (50 Questions)
Solve these real-world challenges online, test your understanding, and reveal instant step-by-step explanations.
1
Short Answer
Hard
2 Marks
In a two-step pattern, terms alternate between 'Multiply by 2' and 'Add 3': 2, 4, 7, 14, 17, [ ? ], [ ? ]. What are the next two terms?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
34 and 37
Step-by-Step Explanation:
From 17: Multiply by 2 -> 34. Then Add 3 -> 37.
2
Short Answer
Hard
2 Marks
Find the sum of the first 6 square numbers: 1² + 2² + 3² + 4² + 5² + 6².
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
1 + 4 + 9 + 16 + 25 + 36 = 91.
3
Short Answer
Hard
2 Marks
How can finding the pattern rule help predict terms far ahead without writing out every intermediate number?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Formulating an algebraic rule (like Term n = Start + (n - 1) × difference) allows direct calculation of any distant term (like the 100th term) in one step.
Step-by-Step Explanation:
Algebraic formulas generalize recursive patterns into direct calculation functions.
4
Short Answer
Hard
2 Marks
Explain the difference between an arithmetic sequence and a geometric sequence using clear examples.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
An arithmetic sequence adds or subtracts a constant common difference (e.g., 3, 7, 11, 15 adds 4), while a geometric sequence multiplies or divides by a constant ratio (e.g., 3, 6, 12, 24 doubles).
Step-by-Step Explanation:
Arithmetic sequences change linearly by addition; geometric sequences grow exponentially by multiplication.
5
Short Answer
Medium
1 Mark
Kevin claims: 'The sequence 2, 4, 8, 16 has the rule Add 2.' Explain Kevin's error and state the true rule.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The rule is multiply by 2 (geometric doubling), not add 2
Step-by-Step Explanation:
Adding 2 only works for 2 to 4; 4+2=6, not 8. Each term is multiplied by 2.
6
Short Answer
Medium
1 Mark
A student writes the sequence of multiples of 9: '9, 18, 27, 35, 45, 54.' Identify the mistake and provide the correct sequence term.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
36 instead of 35
Step-by-Step Explanation:
4 × 9 is 36, not 35.
7
Fill in the Blanks
Medium
1 Mark
Fill in the missing number: 3, 6, 12, [ ? ], 48, 96.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24
Step-by-Step Explanation:
Geometric pattern multiplies by 2: 12 × 2 = 24.
8
Fill in the Blanks
Medium
1 Mark
Find the missing value in this sequence: 14, 21, [ ? ], 35, 42.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28
Step-by-Step Explanation:
Rule is add 7: 21 + 7 = 28.
9
Short Answer
Medium
1 Mark
A bacteria culture doubles in population every hour. If there are 15 cells initially, how many cells will exist after 4 hours?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
240 cells
Step-by-Step Explanation:
Hour 0: 15. Hour 1: 30. Hour 2: 60. Hour 3: 120. Hour 4: 240 cells.
10
Short Answer
Medium
1 Mark
A fitness tracker user logs daily walking goals: Day 1: 4,000 steps, Day 2: 4,500 steps, Day 3: 5,000 steps. What will be the step goal on Day 10?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
8,500 steps
Step-by-Step Explanation:
Rule is +500 steps daily. Day 10 = 4,000 + (9 × 500) = 4,000 + 4,500 = 8,500 steps.
11
Short Answer
Medium
1 Mark
At the Central Botanical Gardens, an amphitheater arranges chairs in rows: Row 1 has 18 chairs, Row 2 has 24, Row 3 has 30, and so on. How many chairs are in Row 7?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
54 chairs
Step-by-Step Explanation:
Pattern starts at 18 with rule +6. Row 7 = 18 + (6 × 6) = 18 + 36 = 54 chairs.
12
Multiple Choice
Easy
1 Mark
Find the 10th term of the sequence starting at 5 with the rule 'Add 4': 5, 9, 13, 17...
A
41
B
45
C
37
D
40
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
41
Step-by-Step Explanation:
Term n = 5 + (n - 1) × 4. For n = 10: 5 + 9 × 4 = 5 + 36 = 41.
13
Multiple Choice
Easy
1 Mark
What is the rule for this sequence: 80, 72, 64, 56, 48?
A
Subtract 8 each time
B
Subtract 6 each time
C
Divide by 2
D
Subtract 10 each time
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Subtract 8 each time
Step-by-Step Explanation:
Each term decreases by 8: 80 - 8 = 72, 72 - 8 = 64, etc.
14
Multiple Choice
Easy
1 Mark
Identify the missing term in the sequence of square numbers: 1, 4, 9, 16, [ ? ], 36.
A
25
B
20
C
24
D
30
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
25
Step-by-Step Explanation:
These are square numbers (1², 2², 3², 4², 5², 6²). 5² = 25.
15
Multiple Choice
Easy
1 Mark
What is the next number in the arithmetic sequence: 27, 38, 49, 60, [ ? ]?
A
71
B
69
C
74
D
82
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
71
Step-by-Step Explanation:
The rule is add 11: 60 + 11 = 71.
16
Short Answer
Hard
2 Marks
In a two-step pattern, terms alternate between 'Multiply by 2' and 'Add 3': 2, 4, 7, 14, 17, [ ? ], [ ? ]. What are the next two terms?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
34 and 37
Step-by-Step Explanation:
From 17: Multiply by 2 -> 34. Then Add 3 -> 37.
17
Short Answer
Hard
2 Marks
Find the sum of the first 6 square numbers: 1² + 2² + 3² + 4² + 5² + 6².
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
1 + 4 + 9 + 16 + 25 + 36 = 91.
18
Short Answer
Hard
2 Marks
How can finding the pattern rule help predict terms far ahead without writing out every intermediate number?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Formulating an algebraic rule (like Term n = Start + (n - 1) × difference) allows direct calculation of any distant term (like the 100th term) in one step.
Step-by-Step Explanation:
Algebraic formulas generalize recursive patterns into direct calculation functions.
19
Short Answer
Hard
2 Marks
Explain the difference between an arithmetic sequence and a geometric sequence using clear examples.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
An arithmetic sequence adds or subtracts a constant common difference (e.g., 3, 7, 11, 15 adds 4), while a geometric sequence multiplies or divides by a constant ratio (e.g., 3, 6, 12, 24 doubles).
Step-by-Step Explanation:
Arithmetic sequences change linearly by addition; geometric sequences grow exponentially by multiplication.
20
Short Answer
Medium
1 Mark
Kevin claims: 'The sequence 2, 4, 8, 16 has the rule Add 2.' Explain Kevin's error and state the true rule.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The rule is multiply by 2 (geometric doubling), not add 2
Step-by-Step Explanation:
Adding 2 only works for 2 to 4; 4+2=6, not 8. Each term is multiplied by 2.
21
Short Answer
Medium
1 Mark
A student writes the sequence of multiples of 9: '9, 18, 27, 35, 45, 54.' Identify the mistake and provide the correct sequence term.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
36 instead of 35
Step-by-Step Explanation:
4 × 9 is 36, not 35.
22
Fill in the Blanks
Medium
1 Mark
Fill in the missing number: 3, 6, 12, [ ? ], 48, 96.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24
Step-by-Step Explanation:
Geometric pattern multiplies by 2: 12 × 2 = 24.
23
Fill in the Blanks
Medium
1 Mark
Find the missing value in this sequence: 14, 21, [ ? ], 35, 42.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28
Step-by-Step Explanation:
Rule is add 7: 21 + 7 = 28.
24
Short Answer
Medium
1 Mark
A bacteria culture doubles in population every hour. If there are 15 cells initially, how many cells will exist after 4 hours?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
240 cells
Step-by-Step Explanation:
Hour 0: 15. Hour 1: 30. Hour 2: 60. Hour 3: 120. Hour 4: 240 cells.
25
Short Answer
Medium
1 Mark
A fitness tracker user logs daily walking goals: Day 1: 4,000 steps, Day 2: 4,500 steps, Day 3: 5,000 steps. What will be the step goal on Day 10?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
8,500 steps
Step-by-Step Explanation:
Rule is +500 steps daily. Day 10 = 4,000 + (9 × 500) = 4,000 + 4,500 = 8,500 steps.
26
Short Answer
Medium
1 Mark
At the Eco-Friendly Solar Park, an amphitheater arranges chairs in rows: Row 1 has 18 chairs, Row 2 has 24, Row 3 has 30, and so on. How many chairs are in Row 7?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
54 chairs
Step-by-Step Explanation:
Pattern starts at 18 with rule +6. Row 7 = 18 + (6 × 6) = 18 + 36 = 54 chairs.
27
Multiple Choice
Easy
1 Mark
Find the 10th term of the sequence starting at 5 with the rule 'Add 4': 5, 9, 13, 17...
A
41
B
45
C
37
D
40
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
41
Step-by-Step Explanation:
Term n = 5 + (n - 1) × 4. For n = 10: 5 + 9 × 4 = 5 + 36 = 41.
28
Multiple Choice
Easy
1 Mark
What is the rule for this sequence: 80, 72, 64, 56, 48?
A
Subtract 8 each time
B
Subtract 6 each time
C
Divide by 2
D
Subtract 10 each time
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Subtract 8 each time
Step-by-Step Explanation:
Each term decreases by 8: 80 - 8 = 72, 72 - 8 = 64, etc.
29
Multiple Choice
Easy
1 Mark
Identify the missing term in the sequence of square numbers: 1, 4, 9, 16, [ ? ], 36.
A
25
B
20
C
24
D
30
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
25
Step-by-Step Explanation:
These are square numbers (1², 2², 3², 4², 5², 6²). 5² = 25.
30
Multiple Choice
Easy
1 Mark
What is the next number in the arithmetic sequence: 24, 34, 44, 54, [ ? ]?
A
64
B
62
C
67
D
74
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
64
Step-by-Step Explanation:
The rule is add 10: 54 + 10 = 64.
31
Short Answer
Hard
2 Marks
In a two-step pattern, terms alternate between 'Multiply by 2' and 'Add 3': 2, 4, 7, 14, 17, [ ? ], [ ? ]. What are the next two terms?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
34 and 37
Step-by-Step Explanation:
From 17: Multiply by 2 -> 34. Then Add 3 -> 37.
32
Short Answer
Hard
2 Marks
Find the sum of the first 6 square numbers: 1² + 2² + 3² + 4² + 5² + 6².
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
1 + 4 + 9 + 16 + 25 + 36 = 91.
33
Short Answer
Hard
2 Marks
How can finding the pattern rule help predict terms far ahead without writing out every intermediate number?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Formulating an algebraic rule (like Term n = Start + (n - 1) × difference) allows direct calculation of any distant term (like the 100th term) in one step.
Step-by-Step Explanation:
Algebraic formulas generalize recursive patterns into direct calculation functions.
34
Short Answer
Hard
2 Marks
Explain the difference between an arithmetic sequence and a geometric sequence using clear examples.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
An arithmetic sequence adds or subtracts a constant common difference (e.g., 3, 7, 11, 15 adds 4), while a geometric sequence multiplies or divides by a constant ratio (e.g., 3, 6, 12, 24 doubles).
Step-by-Step Explanation:
Arithmetic sequences change linearly by addition; geometric sequences grow exponentially by multiplication.
35
Short Answer
Medium
1 Mark
Kevin claims: 'The sequence 2, 4, 8, 16 has the rule Add 2.' Explain Kevin's error and state the true rule.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The rule is multiply by 2 (geometric doubling), not add 2
Step-by-Step Explanation:
Adding 2 only works for 2 to 4; 4+2=6, not 8. Each term is multiplied by 2.
36
Short Answer
Medium
1 Mark
A student writes the sequence of multiples of 9: '9, 18, 27, 35, 45, 54.' Identify the mistake and provide the correct sequence term.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
36 instead of 35
Step-by-Step Explanation:
4 × 9 is 36, not 35.
37
Fill in the Blanks
Medium
1 Mark
Fill in the missing number: 3, 6, 12, [ ? ], 48, 96.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24
Step-by-Step Explanation:
Geometric pattern multiplies by 2: 12 × 2 = 24.
38
Fill in the Blanks
Medium
1 Mark
Find the missing value in this sequence: 14, 21, [ ? ], 35, 42.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28
Step-by-Step Explanation:
Rule is add 7: 21 + 7 = 28.
39
Short Answer
Medium
1 Mark
A bacteria culture doubles in population every hour. If there are 15 cells initially, how many cells will exist after 4 hours?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
240 cells
Step-by-Step Explanation:
Hour 0: 15. Hour 1: 30. Hour 2: 60. Hour 3: 120. Hour 4: 240 cells.
40
Short Answer
Medium
1 Mark
A fitness tracker user logs daily walking goals: Day 1: 4,000 steps, Day 2: 4,500 steps, Day 3: 5,000 steps. What will be the step goal on Day 10?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
8,500 steps
Step-by-Step Explanation:
Rule is +500 steps daily. Day 10 = 4,000 + (9 × 500) = 4,000 + 4,500 = 8,500 steps.
41
Short Answer
Medium
1 Mark
At the Harbor Marine Terminal, an amphitheater arranges chairs in rows: Row 1 has 18 chairs, Row 2 has 24, Row 3 has 30, and so on. How many chairs are in Row 7?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
54 chairs
Step-by-Step Explanation:
Pattern starts at 18 with rule +6. Row 7 = 18 + (6 × 6) = 18 + 36 = 54 chairs.
42
Multiple Choice
Easy
1 Mark
Find the 10th term of the sequence starting at 5 with the rule 'Add 4': 5, 9, 13, 17...
A
41
B
45
C
37
D
40
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
41
Step-by-Step Explanation:
Term n = 5 + (n - 1) × 4. For n = 10: 5 + 9 × 4 = 5 + 36 = 41.
43
Multiple Choice
Easy
1 Mark
What is the rule for this sequence: 80, 72, 64, 56, 48?
A
Subtract 8 each time
B
Subtract 6 each time
C
Divide by 2
D
Subtract 10 each time
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Subtract 8 each time
Step-by-Step Explanation:
Each term decreases by 8: 80 - 8 = 72, 72 - 8 = 64, etc.
44
Multiple Choice
Easy
1 Mark
Identify the missing term in the sequence of square numbers: 1, 4, 9, 16, [ ? ], 36.
A
25
B
20
C
24
D
30
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
25
Step-by-Step Explanation:
These are square numbers (1², 2², 3², 4², 5², 6²). 5² = 25.
45
Multiple Choice
Easy
1 Mark
What is the next number in the arithmetic sequence: 21, 30, 39, 48, [ ? ]?
A
57
B
55
C
60
D
66
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
57
Step-by-Step Explanation:
The rule is add 9: 48 + 9 = 57.
46
Short Answer
Hard
2 Marks
In a two-step pattern, terms alternate between 'Multiply by 2' and 'Add 3': 2, 4, 7, 14, 17, [ ? ], [ ? ]. What are the next two terms?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
34 and 37
Step-by-Step Explanation:
From 17: Multiply by 2 -> 34. Then Add 3 -> 37.
47
Short Answer
Hard
2 Marks
Find the sum of the first 6 square numbers: 1² + 2² + 3² + 4² + 5² + 6².
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
91
Step-by-Step Explanation:
1 + 4 + 9 + 16 + 25 + 36 = 91.
48
Short Answer
Hard
2 Marks
How can finding the pattern rule help predict terms far ahead without writing out every intermediate number?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Formulating an algebraic rule (like Term n = Start + (n - 1) × difference) allows direct calculation of any distant term (like the 100th term) in one step.
Step-by-Step Explanation:
Algebraic formulas generalize recursive patterns into direct calculation functions.
49
Short Answer
Hard
2 Marks
Explain the difference between an arithmetic sequence and a geometric sequence using clear examples.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
An arithmetic sequence adds or subtracts a constant common difference (e.g., 3, 7, 11, 15 adds 4), while a geometric sequence multiplies or divides by a constant ratio (e.g., 3, 6, 12, 24 doubles).
Step-by-Step Explanation:
Arithmetic sequences change linearly by addition; geometric sequences grow exponentially by multiplication.
50
Short Answer
Medium
1 Mark
Kevin claims: 'The sequence 2, 4, 8, 16 has the rule Add 2.' Explain Kevin's error and state the true rule.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The rule is multiply by 2 (geometric doubling), not add 2
Step-by-Step Explanation:
Adding 2 only works for 2 to 4; 4+2=6, not 8. Each term is multiplied by 2.