Number Patterns (Grade 5)
A number pattern is a sequence of numbers that follows a specific rule. In Class 5, you learn to identify, describe, and extend patterns that involve addition, subtraction, multiplication, division, and combinations of these operations.
Recognising patterns is a fundamental skill in mathematics. It helps build logical thinking and prepares you for algebra, where rules are expressed using variables.
Number patterns appear everywhere — in the calendar, in multiplication tables, in nature (petals on flowers), and in music (beats and rhythms).
What is Number Patterns - Class 5 Maths (Patterns and Algebra)?
A number pattern (or sequence) is an ordered list of numbers where each number follows a definite rule from the previous one.
Key terms:
- Term — each number in the pattern
- Rule — the operation that generates each term from the previous one
- Common difference — the constant added or subtracted (in arithmetic patterns)
- Common ratio — the constant multiplied or divided (in geometric patterns)
Types and Properties
Types of Number Patterns:
- Arithmetic pattern: Each term is obtained by adding or subtracting a fixed number. Example: 3, 7, 11, 15, 19 (rule: add 4).
- Geometric pattern: Each term is obtained by multiplying or dividing by a fixed number. Example: 2, 6, 18, 54 (rule: multiply by 3).
- Triangular numbers: 1, 3, 6, 10, 15, 21 (differences increase by 1 each time).
- Square numbers: 1, 4, 9, 16, 25, 36 (each term = n²).
- Fibonacci-like pattern: Each term is the sum of the two before it. Example: 1, 1, 2, 3, 5, 8, 13.
Solved Examples
Example 1: Example 1: Arithmetic Pattern (Addition)
Problem: Find the next 3 terms: 5, 11, 17, 23, __, __, __
Solution:
Step 1: Find the rule: 11 − 5 = 6, 17 − 11 = 6, 23 − 17 = 6. Rule: add 6.
Step 2: 23 + 6 = 29, 29 + 6 = 35, 35 + 6 = 41
Answer: 5, 11, 17, 23, 29, 35, 41
Example 2: Example 2: Arithmetic Pattern (Subtraction)
Problem: Find the next 3 terms: 100, 92, 84, 76, __, __, __
Solution:
Step 1: 92 − 100 = −8. Rule: subtract 8.
Step 2: 76 − 8 = 68, 68 − 8 = 60, 60 − 8 = 52
Answer: 100, 92, 84, 76, 68, 60, 52
Example 3: Example 3: Geometric Pattern (Multiplication)
Problem: Find the next 3 terms: 3, 9, 27, 81, __, __, __
Solution:
Step 1: 9 ÷ 3 = 3, 27 ÷ 9 = 3. Rule: multiply by 3.
Step 2: 81 × 3 = 243, 243 × 3 = 729, 729 × 3 = 2,187
Answer: 3, 9, 27, 81, 243, 729, 2187
Example 4: Example 4: Two-Step Rule
Problem: Find the rule and next 2 terms: 2, 5, 11, 23, 47, __, __
Solution:
Step 1: 2 × 2 + 1 = 5, 5 × 2 + 1 = 11, 11 × 2 + 1 = 23, 23 × 2 + 1 = 47. Rule: multiply by 2 then add 1.
Step 2: 47 × 2 + 1 = 95, 95 × 2 + 1 = 191
Answer: Next terms: 95, 191
Example 5: Example 5: Square Numbers
Problem: Identify the pattern: 1, 4, 9, 16, 25, __. What is the next term?
Solution:
Step 1: 1 = 1², 4 = 2², 9 = 3², 16 = 4², 25 = 5²
Step 2: Next term = 6² = 36
Answer: The next term is 36. These are square numbers.
Example 6: Example 6: Triangular Numbers
Problem: Find the next 2 terms: 1, 3, 6, 10, 15, __, __
Solution:
Step 1: Differences: 2, 3, 4, 5 — each difference increases by 1.
Step 2: Next difference = 6: 15 + 6 = 21
Step 3: Next difference = 7: 21 + 7 = 28
Answer: Next terms: 21, 28
Example 7: Example 7: Finding a Missing Term
Problem: Find the missing number: 8, 15, __, 29, 36
Solution:
Step 1: 15 − 8 = 7, 36 − 29 = 7. Rule: add 7.
Step 2: Missing term = 15 + 7 = 22
Answer: Missing number = 22
Example 8: Example 8: Division Pattern
Problem: Find the next 3 terms: 6400, 1600, 400, 100, __, __, __
Solution:
Step 1: 6400 ÷ 4 = 1600, 1600 ÷ 4 = 400, 400 ÷ 4 = 100. Rule: divide by 4.
Step 2: 100 ÷ 4 = 25, 25 ÷ 4 = 6.25, 6.25 ÷ 4 = 1.5625
Answer: Next terms: 25, 6.25, 1.5625
Example 9: Example 9: Finding the nth Term
Problem: In the pattern 4, 7, 10, 13, 16, ... what is the 10th term?
Solution:
Step 1: Rule: start at 4, add 3 each time.
Step 2: The nth term = 4 + (n − 1) × 3
Step 3: 10th term = 4 + 9 × 3 = 4 + 27 = 31
Answer: The 10th term is 31.
Key Points to Remember
- A number pattern follows a specific rule.
- To find the rule, look at the difference or ratio between consecutive terms.
- Arithmetic patterns have a constant difference (add or subtract).
- Geometric patterns have a constant ratio (multiply or divide).
- Square numbers: 1, 4, 9, 16, 25, 36, ... (n × n).
- Triangular numbers: 1, 3, 6, 10, 15, 21, ... (differences increase by 1).
- Some patterns have a two-step rule (e.g., multiply by 2 then add 1).
Practice Problems
- Find the next 3 terms: 7, 14, 21, 28, __, __, __
- What is the rule for the pattern 2, 6, 18, 54, 162? Find the next term.
- Complete the pattern: 1000, 900, 800, __, __, __
- Identify the pattern and find the missing number: 5, 10, 20, __, 80, 160
- Ria writes the pattern 1, 4, 9, 16, 25. What type of numbers are these? What is the 8th term?
- Find the 12th term of the pattern: 3, 8, 13, 18, 23, ...
- The pattern is: 1, 1, 2, 3, 5, 8, 13. What are the next two terms?
- Write the first 6 triangular numbers.
Frequently Asked Questions
Q1. What is a number pattern?
A number pattern is a sequence of numbers following a specific rule. The rule determines how each number is obtained from the previous one.
Q2. How do you find the rule of a pattern?
Look at the difference between consecutive terms. If it is constant, the rule is adding or subtracting. If the ratio is constant, the rule is multiplying or dividing. Some patterns combine operations.
Q3. What are square numbers?
Square numbers are obtained by multiplying a number by itself: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. The nth square number is n × n.
Q4. What are triangular numbers?
Triangular numbers are 1, 3, 6, 10, 15, 21, 28, ... Each term adds one more than the previous difference. They can be visualised as dots forming a triangle.
Q5. What is the Fibonacci pattern?
In a Fibonacci-like pattern, each term is the sum of the two terms before it. Example: 1, 1, 2, 3, 5, 8, 13, 21. It appears in nature — in flower petals and seashells.
Q6. Can patterns involve decimals or fractions?
Yes. Patterns can use any type of number. For example: 0.5, 1.0, 1.5, 2.0, 2.5 (rule: add 0.5) or 1/2, 1/4, 1/8 (rule: divide by 2).
Q7. How do you find a specific term (like the 20th term)?
For arithmetic patterns, use the formula: nth term = first term + (n − 1) × common difference. For example, in 5, 8, 11, 14, ... the 20th term = 5 + 19 × 3 = 62.
Q8. Why are patterns important in mathematics?
Patterns build logical thinking and are the foundation of algebra. Recognising patterns helps solve problems efficiently and is used in computer science, music, and nature.
