Lesson 3.1: Repeating and Growing Patterns: Shapes and Numbers
Identify repeating cores (AB, AAB, ABC) and growing sequences where terms increase or decrease by consistent rules.
⏱️ Reading Time: 15 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Patterns and Sequences
A textile artisan weaves traditional geometric carpets. She sets up an alternating border pattern: 2 blue triangles, 1 golden diamond, 2 blue triangles, 1 golden diamond. By identifying the core unit (AAB), she calculates the yarn required for 100 repeats.
💡 Core Mathematical Concepts: Repeating & Growing Patterns
Focus areas: Repeating unit, growing pattern, core pattern, sequence, step size.
| Concept / Term | Mathematical Definition | Everyday Example |
|---|---|---|
| Repeating Pattern | A sequence that repeats a fixed group of elements (the core) indefinitely | Circle, Square, Triangle, Circle, Square, Triangle (ABC pattern) |
| Growing Pattern | A sequence where each term grows or shrinks by a mathematical rule | 3, 6, 9, 12, 15 (Rule: Add 3 each time) |
| Pattern Core | The shortest repeating block of elements that creates the full sequence | In ▲▲■▲▲■▲▲■, the core is ▲▲■ (length 3) |
| Two-Step Rules | Sequences using two alternating operations (e.g., +2, +3, +2, +3) | 2, 4, 7, 9, 12, 14, 17... |
🔍 Practical Classroom & Everyday Examples
Example 1: Finding Next Term in Growing Sequences
Subtract the first term from the second term to find the common difference: 14 - 8 = 6. Check if 20 - 14 = 6.
Example 2: Predicting Distant Repeating Terms
Use division with remainders! For a 3-element core, the 10th term corresponds to 10 ÷ 3 = 3 R 1 (the 1st element of the core).
⚠️ Watch Out! Common Mistakes to Avoid
Common Error: Assuming a pattern grows by 1 without checking
Correction: Always compute the difference between at least two pairs of consecutive numbers.
Common Error: Confusing repeating patterns with growing patterns
Correction: Repeating patterns cycle through identical shapes; growing patterns increase in size or number.
🎯 Quick Self-Check Challenge
In the repeating shape pattern: ★, ●, ■, ▲, ★, ●, ■, ▲... what is the 17th shape in the sequence?
Answer & Explanation:
The core has 4 shapes (★, ●, ■, ▲). 17 ÷ 4 = 4 full repeats with a remainder of 1. The 1st shape in the core is ★.
🎯 Key Learning Takeaways
Master Patterns and Sequences fundamentals.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G3-M-CH03-WS05
A4 • 15 Qs
Patterns and Sequences — Worksheet 5
Growing Sequences, Parity & Algebraic Rules (Space Colony Solar Array)
G3-M-CH03-WS04
A4 • 15 Qs
Patterns and Sequences — Worksheet 4
Growing Sequences, Parity & Algebraic Rules (Musical Rhythm Patterns)
G3-M-CH03-WS03
A4 • 15 Qs
Patterns and Sequences — Worksheet 3
Growing Sequences, Parity & Algebraic Rules (Computer Code Generator)
G3-M-CH03-WS02
A4 • 15 Qs
Patterns and Sequences — Worksheet 2
Growing Sequences, Parity & Algebraic Rules (Orchard Planting Rows)
G3-M-CH03-WS01
A4 • 15 Qs
Patterns and Sequences — Worksheet 1
Growing Sequences, Parity & Algebraic Rules (Ceramic Tile Factory)
✍️ 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 sequence where the rule is 'Multiply by 2 and subtract 1', the first term is 3. What is the 4th term?
A
17
B
9
C
33
D
25
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
17
Step-by-Step Explanation:
Term 1: 3. Term 2: (3 × 2) - 1 = 5. Term 3: (5 × 2) - 1 = 9. Term 4: (9 × 2) - 1 = 17.
2
Short Answer
Hard
2 Marks
A baker stacks cupcakes in a triangle display: 1 cupcake in top tier, 3 in second, 6 in third, 10 in fourth, 15 in fifth. How many cupcakes will be in the 7th tier?
A
28 cupcakes
B
21 cupcakes
C
36 cupcakes
D
25 cupcakes
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 cupcakes
Step-by-Step Explanation:
Triangular numbers: tier 6 has 15 + 6 = 21 cupcakes; tier 7 has 21 + 7 = 28 cupcakes.
3
Short Answer
Hard
2 Marks
In the number sequence starting at 1 where every term adds 2 (1, 3, 5, 7, 9...), will the number 500 ever appear in this sequence?
A
No, because all numbers in this sequence are odd, and 500 is an even number
B
Yes, if the sequence continues long enough
C
Yes, because 500 is divisible by 5
D
No, because the sequence stops at 100
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
No, because all numbers in this sequence are odd, and 500 is an even number
Step-by-Step Explanation:
Starting with an odd number and repeatedly adding 2 generates only odd numbers. 500 is even.
4
Short Answer
Hard
2 Marks
Why does adding two odd numbers always produce an even sum? (e.g., 2n+1 + 2m+1)
A
Each odd number has an extra 'leftover' 1 when paired in twos; the two leftovers pair up to make an exact pair, leaving no remainder
B
Because odd numbers are larger than even numbers
C
By coincidence for numbers under 100
D
Because addition is the opposite of subtraction
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Each odd number has an extra 'leftover' 1 when paired in twos; the two leftovers pair up to make an exact pair, leaving no remainder
Step-by-Step Explanation:
Each odd number has 1 unpaired remainder. When added together, 1 + 1 = 2, completing an exact pair.
5
Short Answer
Medium
1 Mark
Farah claims: 'Because 24 is even and 15 is odd, their product 24 × 15 must be odd.' What is Farah's mistake?
A
Even × Odd is always EVEN (24 × 15 = 360, which ends in 0)
B
24 × 15 is a prime number
C
15 is an even number
D
Both numbers are odd
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Even × Odd is always EVEN (24 × 15 = 360, which ends in 0)
Step-by-Step Explanation:
Any number multiplied by an even number yields an even product.
6
Short Answer
Medium
1 Mark
A student writes: 'The sequence 5, 10, 20, 35, 55 has a rule of adding 5 each time.' What is the error in this statement?
A
The numbers do not increase by 5 each time; the differences are +5, +10, +15, +20 (growing differences)
B
The sequence is decreasing
C
All the numbers are odd
D
The first number should be 0
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The numbers do not increase by 5 each time; the differences are +5, +10, +15, +20 (growing differences)
Step-by-Step Explanation:
The differences grow by 5 each step (+5, +10, +15, +20), rather than a constant difference of 5.
7
Fill in the Blanks
Medium
1 Mark
Solve the two-step pattern: 4, 7, 6, 9, 8, 11, [ ? ]
A
10
B
12
C
9
D
13
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
10
Step-by-Step Explanation:
The pattern alternates: +3, -1, +3, -1, +3, -1. 11 - 1 = 10.
8
Fill in the Blanks
Medium
1 Mark
Find the missing term in the sequence: 21, [ ? ], 35, 42, 49
A
28
B
27
C
30
D
23
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28
Step-by-Step Explanation:
21 + 7 = 28.
9
Short Answer
Medium
1 Mark
A library arranges shelves with alternating color stickers: Red, Blue, Green, Yellow, Red, Blue, Green, Yellow... What color sticker is placed on the 26th shelf?
A
Blue
B
Red
C
Green
D
Yellow
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Blue
Step-by-Step Explanation:
Core length is 4. 26 ÷ 4 = 6 R 2. The 2nd color in the core is Blue.
10
Short Answer
Medium
1 Mark
A runner trains by running laps: Day 1 (3 laps), Day 2 (6 laps), Day 3 (9 laps), Day 4 (12 laps). Following this pattern, how many laps will the runner complete on Day 7?
A
21 laps
B
18 laps
C
24 laps
D
27 laps
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
21 laps
Step-by-Step Explanation:
The rule is 3 × Day number: 7 × 3 = 21 laps.
11
Short Answer
Medium
1 Mark
At the Space Colony Solar Array, an engineer places solar panels in rows: Row 1 has 21 panels, Row 2 has 28, Row 3 has 35. How many panels will be installed in Row 5?
A
49 panels
B
47 panels
C
52 panels
D
56 panels
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
49 panels
Step-by-Step Explanation:
Each row increases by 7: Row 4 = 42, Row 5 = 49 panels.
12
Multiple Choice
Easy
1 Mark
In a repeating shape pattern with a 3-element core (▲, ■, ●), what is the 12th shape?
A
● (the 3rd shape)
B
▲ (the 1st shape)
C
■ (the 2nd shape)
D
★ (a new shape)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
● (the 3rd shape)
Step-by-Step Explanation:
12 ÷ 3 = 4 with remainder 0. When remainder is 0, it is the last shape of the core (●).
13
Multiple Choice
Easy
1 Mark
What is the sum of any two odd numbers (e.g., 7 + 11)?
A
Always an even number
B
Always an odd number
C
Sometimes odd, sometimes even
D
Always a multiple of 10
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Always an even number
Step-by-Step Explanation:
Odd + Odd = Even (e.g., 7 + 11 = 18).
14
Multiple Choice
Easy
1 Mark
Which of the following numbers is an ODD number?
A
347
B
348
C
350
D
342
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
347
Step-by-Step Explanation:
Odd numbers end in 1, 3, 5, 7, or 9. 347 ends in 7.
15
Multiple Choice
Easy
1 Mark
Find the next number in the sequence: 21, 28, 35, 42, [ ? ]
A
49
B
48
C
51
D
56
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
49
Step-by-Step Explanation:
The rule is add 7: 42 + 7 = 49.
16
Short Answer
Hard
2 Marks
In a sequence where the rule is 'Multiply by 2 and subtract 1', the first term is 3. What is the 4th term?
A
17
B
9
C
33
D
25
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
17
Step-by-Step Explanation:
Term 1: 3. Term 2: (3 × 2) - 1 = 5. Term 3: (5 × 2) - 1 = 9. Term 4: (9 × 2) - 1 = 17.
17
Short Answer
Hard
2 Marks
A baker stacks cupcakes in a triangle display: 1 cupcake in top tier, 3 in second, 6 in third, 10 in fourth, 15 in fifth. How many cupcakes will be in the 7th tier?
A
28 cupcakes
B
21 cupcakes
C
36 cupcakes
D
25 cupcakes
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 cupcakes
Step-by-Step Explanation:
Triangular numbers: tier 6 has 15 + 6 = 21 cupcakes; tier 7 has 21 + 7 = 28 cupcakes.
18
Short Answer
Hard
2 Marks
In the number sequence starting at 1 where every term adds 2 (1, 3, 5, 7, 9...), will the number 500 ever appear in this sequence?
A
No, because all numbers in this sequence are odd, and 500 is an even number
B
Yes, if the sequence continues long enough
C
Yes, because 500 is divisible by 5
D
No, because the sequence stops at 100
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
No, because all numbers in this sequence are odd, and 500 is an even number
Step-by-Step Explanation:
Starting with an odd number and repeatedly adding 2 generates only odd numbers. 500 is even.
19
Short Answer
Hard
2 Marks
Why does adding two odd numbers always produce an even sum? (e.g., 2n+1 + 2m+1)
A
Each odd number has an extra 'leftover' 1 when paired in twos; the two leftovers pair up to make an exact pair, leaving no remainder
B
Because odd numbers are larger than even numbers
C
By coincidence for numbers under 100
D
Because addition is the opposite of subtraction
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Each odd number has an extra 'leftover' 1 when paired in twos; the two leftovers pair up to make an exact pair, leaving no remainder
Step-by-Step Explanation:
Each odd number has 1 unpaired remainder. When added together, 1 + 1 = 2, completing an exact pair.
20
Short Answer
Medium
1 Mark
Farah claims: 'Because 24 is even and 15 is odd, their product 24 × 15 must be odd.' What is Farah's mistake?
A
Even × Odd is always EVEN (24 × 15 = 360, which ends in 0)
B
24 × 15 is a prime number
C
15 is an even number
D
Both numbers are odd
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Even × Odd is always EVEN (24 × 15 = 360, which ends in 0)
Step-by-Step Explanation:
Any number multiplied by an even number yields an even product.
21
Short Answer
Medium
1 Mark
A student writes: 'The sequence 5, 10, 20, 35, 55 has a rule of adding 5 each time.' What is the error in this statement?
A
The numbers do not increase by 5 each time; the differences are +5, +10, +15, +20 (growing differences)
B
The sequence is decreasing
C
All the numbers are odd
D
The first number should be 0
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The numbers do not increase by 5 each time; the differences are +5, +10, +15, +20 (growing differences)
Step-by-Step Explanation:
The differences grow by 5 each step (+5, +10, +15, +20), rather than a constant difference of 5.
22
Fill in the Blanks
Medium
1 Mark
Solve the two-step pattern: 4, 7, 6, 9, 8, 11, [ ? ]
A
10
B
12
C
9
D
13
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
10
Step-by-Step Explanation:
The pattern alternates: +3, -1, +3, -1, +3, -1. 11 - 1 = 10.
23
Fill in the Blanks
Medium
1 Mark
Find the missing term in the sequence: 9, [ ? ], 15, 18, 21
A
12
B
11
C
14
D
11
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
12
Step-by-Step Explanation:
9 + 3 = 12.
24
Short Answer
Medium
1 Mark
A library arranges shelves with alternating color stickers: Red, Blue, Green, Yellow, Red, Blue, Green, Yellow... What color sticker is placed on the 26th shelf?
A
Blue
B
Red
C
Green
D
Yellow
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Blue
Step-by-Step Explanation:
Core length is 4. 26 ÷ 4 = 6 R 2. The 2nd color in the core is Blue.
25
Short Answer
Medium
1 Mark
A runner trains by running laps: Day 1 (3 laps), Day 2 (6 laps), Day 3 (9 laps), Day 4 (12 laps). Following this pattern, how many laps will the runner complete on Day 7?
A
21 laps
B
18 laps
C
24 laps
D
27 laps
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
21 laps
Step-by-Step Explanation:
The rule is 3 × Day number: 7 × 3 = 21 laps.
26
Short Answer
Medium
1 Mark
At the Musical Rhythm Patterns, an engineer places solar panels in rows: Row 1 has 9 panels, Row 2 has 12, Row 3 has 15. How many panels will be installed in Row 5?
A
21 panels
B
19 panels
C
24 panels
D
24 panels
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
21 panels
Step-by-Step Explanation:
Each row increases by 3: Row 4 = 18, Row 5 = 21 panels.
27
Multiple Choice
Easy
1 Mark
In a repeating shape pattern with a 3-element core (▲, ■, ●), what is the 12th shape?
A
● (the 3rd shape)
B
▲ (the 1st shape)
C
■ (the 2nd shape)
D
★ (a new shape)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
● (the 3rd shape)
Step-by-Step Explanation:
12 ÷ 3 = 4 with remainder 0. When remainder is 0, it is the last shape of the core (●).
28
Multiple Choice
Easy
1 Mark
What is the sum of any two odd numbers (e.g., 7 + 11)?
A
Always an even number
B
Always an odd number
C
Sometimes odd, sometimes even
D
Always a multiple of 10
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Always an even number
Step-by-Step Explanation:
Odd + Odd = Even (e.g., 7 + 11 = 18).
29
Multiple Choice
Easy
1 Mark
Which of the following numbers is an ODD number?
A
347
B
348
C
350
D
342
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
347
Step-by-Step Explanation:
Odd numbers end in 1, 3, 5, 7, or 9. 347 ends in 7.
30
Multiple Choice
Easy
1 Mark
Find the next number in the sequence: 9, 12, 15, 18, [ ? ]
A
21
B
20
C
23
D
24
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
21
Step-by-Step Explanation:
The rule is add 3: 18 + 3 = 21.
31
Short Answer
Hard
2 Marks
In a sequence where the rule is 'Multiply by 2 and subtract 1', the first term is 3. What is the 4th term?
A
17
B
9
C
33
D
25
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
17
Step-by-Step Explanation:
Term 1: 3. Term 2: (3 × 2) - 1 = 5. Term 3: (5 × 2) - 1 = 9. Term 4: (9 × 2) - 1 = 17.
32
Short Answer
Hard
2 Marks
A baker stacks cupcakes in a triangle display: 1 cupcake in top tier, 3 in second, 6 in third, 10 in fourth, 15 in fifth. How many cupcakes will be in the 7th tier?
A
28 cupcakes
B
21 cupcakes
C
36 cupcakes
D
25 cupcakes
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 cupcakes
Step-by-Step Explanation:
Triangular numbers: tier 6 has 15 + 6 = 21 cupcakes; tier 7 has 21 + 7 = 28 cupcakes.
33
Short Answer
Hard
2 Marks
In the number sequence starting at 1 where every term adds 2 (1, 3, 5, 7, 9...), will the number 500 ever appear in this sequence?
A
No, because all numbers in this sequence are odd, and 500 is an even number
B
Yes, if the sequence continues long enough
C
Yes, because 500 is divisible by 5
D
No, because the sequence stops at 100
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
No, because all numbers in this sequence are odd, and 500 is an even number
Step-by-Step Explanation:
Starting with an odd number and repeatedly adding 2 generates only odd numbers. 500 is even.
34
Short Answer
Hard
2 Marks
Why does adding two odd numbers always produce an even sum? (e.g., 2n+1 + 2m+1)
A
Each odd number has an extra 'leftover' 1 when paired in twos; the two leftovers pair up to make an exact pair, leaving no remainder
B
Because odd numbers are larger than even numbers
C
By coincidence for numbers under 100
D
Because addition is the opposite of subtraction
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Each odd number has an extra 'leftover' 1 when paired in twos; the two leftovers pair up to make an exact pair, leaving no remainder
Step-by-Step Explanation:
Each odd number has 1 unpaired remainder. When added together, 1 + 1 = 2, completing an exact pair.
35
Short Answer
Medium
1 Mark
Farah claims: 'Because 24 is even and 15 is odd, their product 24 × 15 must be odd.' What is Farah's mistake?
A
Even × Odd is always EVEN (24 × 15 = 360, which ends in 0)
B
24 × 15 is a prime number
C
15 is an even number
D
Both numbers are odd
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Even × Odd is always EVEN (24 × 15 = 360, which ends in 0)
Step-by-Step Explanation:
Any number multiplied by an even number yields an even product.
36
Short Answer
Medium
1 Mark
A student writes: 'The sequence 5, 10, 20, 35, 55 has a rule of adding 5 each time.' What is the error in this statement?
A
The numbers do not increase by 5 each time; the differences are +5, +10, +15, +20 (growing differences)
B
The sequence is decreasing
C
All the numbers are odd
D
The first number should be 0
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The numbers do not increase by 5 each time; the differences are +5, +10, +15, +20 (growing differences)
Step-by-Step Explanation:
The differences grow by 5 each step (+5, +10, +15, +20), rather than a constant difference of 5.
37
Fill in the Blanks
Medium
1 Mark
Solve the two-step pattern: 4, 7, 6, 9, 8, 11, [ ? ]
A
10
B
12
C
9
D
13
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
10
Step-by-Step Explanation:
The pattern alternates: +3, -1, +3, -1, +3, -1. 11 - 1 = 10.
38
Fill in the Blanks
Medium
1 Mark
Find the missing term in the sequence: 15, [ ? ], 25, 30, 35
A
20
B
19
C
22
D
17
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
20
Step-by-Step Explanation:
15 + 5 = 20.
39
Short Answer
Medium
1 Mark
A library arranges shelves with alternating color stickers: Red, Blue, Green, Yellow, Red, Blue, Green, Yellow... What color sticker is placed on the 26th shelf?
A
Blue
B
Red
C
Green
D
Yellow
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Blue
Step-by-Step Explanation:
Core length is 4. 26 ÷ 4 = 6 R 2. The 2nd color in the core is Blue.
40
Short Answer
Medium
1 Mark
A runner trains by running laps: Day 1 (3 laps), Day 2 (6 laps), Day 3 (9 laps), Day 4 (12 laps). Following this pattern, how many laps will the runner complete on Day 7?
A
21 laps
B
18 laps
C
24 laps
D
27 laps
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
21 laps
Step-by-Step Explanation:
The rule is 3 × Day number: 7 × 3 = 21 laps.
41
Short Answer
Medium
1 Mark
At the Computer Code Generator, an engineer places solar panels in rows: Row 1 has 15 panels, Row 2 has 20, Row 3 has 25. How many panels will be installed in Row 5?
A
35 panels
B
33 panels
C
38 panels
D
40 panels
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
35 panels
Step-by-Step Explanation:
Each row increases by 5: Row 4 = 30, Row 5 = 35 panels.
42
Multiple Choice
Easy
1 Mark
In a repeating shape pattern with a 3-element core (▲, ■, ●), what is the 12th shape?
A
● (the 3rd shape)
B
▲ (the 1st shape)
C
■ (the 2nd shape)
D
★ (a new shape)
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
● (the 3rd shape)
Step-by-Step Explanation:
12 ÷ 3 = 4 with remainder 0. When remainder is 0, it is the last shape of the core (●).
43
Multiple Choice
Easy
1 Mark
What is the sum of any two odd numbers (e.g., 7 + 11)?
A
Always an even number
B
Always an odd number
C
Sometimes odd, sometimes even
D
Always a multiple of 10
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Always an even number
Step-by-Step Explanation:
Odd + Odd = Even (e.g., 7 + 11 = 18).
44
Multiple Choice
Easy
1 Mark
Which of the following numbers is an ODD number?
A
347
B
348
C
350
D
342
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
347
Step-by-Step Explanation:
Odd numbers end in 1, 3, 5, 7, or 9. 347 ends in 7.
45
Multiple Choice
Easy
1 Mark
Find the next number in the sequence: 15, 20, 25, 30, [ ? ]
A
35
B
34
C
37
D
40
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
35
Step-by-Step Explanation:
The rule is add 5: 30 + 5 = 35.
46
Short Answer
Hard
2 Marks
In a sequence where the rule is 'Multiply by 2 and subtract 1', the first term is 3. What is the 4th term?
A
17
B
9
C
33
D
25
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
17
Step-by-Step Explanation:
Term 1: 3. Term 2: (3 × 2) - 1 = 5. Term 3: (5 × 2) - 1 = 9. Term 4: (9 × 2) - 1 = 17.
47
Short Answer
Hard
2 Marks
A baker stacks cupcakes in a triangle display: 1 cupcake in top tier, 3 in second, 6 in third, 10 in fourth, 15 in fifth. How many cupcakes will be in the 7th tier?
A
28 cupcakes
B
21 cupcakes
C
36 cupcakes
D
25 cupcakes
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 cupcakes
Step-by-Step Explanation:
Triangular numbers: tier 6 has 15 + 6 = 21 cupcakes; tier 7 has 21 + 7 = 28 cupcakes.
48
Short Answer
Hard
2 Marks
In the number sequence starting at 1 where every term adds 2 (1, 3, 5, 7, 9...), will the number 500 ever appear in this sequence?
A
No, because all numbers in this sequence are odd, and 500 is an even number
B
Yes, if the sequence continues long enough
C
Yes, because 500 is divisible by 5
D
No, because the sequence stops at 100
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
No, because all numbers in this sequence are odd, and 500 is an even number
Step-by-Step Explanation:
Starting with an odd number and repeatedly adding 2 generates only odd numbers. 500 is even.
49
Short Answer
Hard
2 Marks
Why does adding two odd numbers always produce an even sum? (e.g., 2n+1 + 2m+1)
A
Each odd number has an extra 'leftover' 1 when paired in twos; the two leftovers pair up to make an exact pair, leaving no remainder
B
Because odd numbers are larger than even numbers
C
By coincidence for numbers under 100
D
Because addition is the opposite of subtraction
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Correct Answer:
Each odd number has an extra 'leftover' 1 when paired in twos; the two leftovers pair up to make an exact pair, leaving no remainder
Step-by-Step Explanation:
Each odd number has 1 unpaired remainder. When added together, 1 + 1 = 2, completing an exact pair.
50
Short Answer
Medium
1 Mark
Farah claims: 'Because 24 is even and 15 is odd, their product 24 × 15 must be odd.' What is Farah's mistake?
A
Even × Odd is always EVEN (24 × 15 = 360, which ends in 0)
B
24 × 15 is a prime number
C
15 is an even number
D
Both numbers are odd
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Correct Answer:
Even × Odd is always EVEN (24 × 15 = 360, which ends in 0)
Step-by-Step Explanation:
Any number multiplied by an even number yields an even product.