Number and Sequences Worksheet — KS3 — Beginner
Number and Sequences worksheet for Key Stage 3 / Year 7-9 (Ages 11-14). Beginner level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.
Exploring Numbers and Sequences
Key Stage 3 / Ages 11-14 / Beginner
Instructions: This worksheet will guide you through understanding number patterns and sequences. You'll solve equations, identify patterns, and complete sequences. Follow the instructions for each activity and fill in the answers in the provided spaces.
Identifying Arithmetic Sequences
Examine each sequence and determine the common difference. Write the next two numbers in the sequence. Use the space provided to show your working.
1. 3, 6, 9, 12, ...
2. 10, 15, 20, 25, ...
3. 2, 5, 8, 11, ...
4. 7, 14, 21, 28, ...
5. 1, 4, 7, 10, ...
Finding the nth Term
For each arithmetic sequence, find the formula for the nth term. Use the formula to calculate the 10th term.
1. 5, 8, 11, 14, ...
2. 2, 6, 10, 14, ...
3. 9, 12, 15, 18, ...
4. 4, 9, 14, 19, ...
Exploring Geometric Sequences
Identify the common ratio in each geometric sequence and write the next two terms. Show your calculations in the space provided.
1. 2, 4, 8, 16, ...
2. 3, 9, 27, 81, ...
3. 5, 25, 125, 625, ...
4. 10, 50, 250, 1250, ...
Solving Linear Equations
Solve each equation for x. Show all your working clearly in the space provided.
1. 2x + 3 = 11
2. 4x - 5 = 19
3. 3x + 7 = 22
4. 5x - 9 = 26
Completing Number Patterns
Complete each number pattern by identifying the rule and writing the next three numbers. Use the space provided for your answers.
1. 1, 4, 9, 16, ...
2. 2, 5, 10, 17, ...
3. 3, 8, 15, 24, ...
4. 4, 12, 24, 40, ...
Data Analysis with Sequences
Analyse the data in the table and answer the questions below. Calculate the missing values and fill in the blanks.
| Sequence | 1st Term | 2nd Term | 3rd Term |
| A | 3 | 6 | 9 |
| B | 5 | 10 | 15 |
| C | 7 | 14 | |
| D | 9 | 27 |
1. What is the missing value in sequence C?
2. Calculate the missing value in sequence D.
Exploring Fibonacci Sequences
The Fibonacci sequence is a famous number pattern. Each number is the sum of the two preceding ones. Write the next three numbers in the sequence.
1. 0, 1, 1, 2, 3, 5, ...
2. 1, 1, 2, 3, 5, 8, ...
Creating Your Own Sequence
Create your own arithmetic sequence. Write the first five terms and explain the rule you used. Use the space provided for your explanation.
1. First five terms:
2. Explanation of the rule:
Activity 1: 15, 18 ; 30, 35 ; 14, 17 ; 35, 42 ; 13, 16
Activity 2: 3n + 2 ; 4n - 2 ; 3n + 6 ; 5n - 1
Activity 3: 32, 64 ; 243, 729 ; 3125, 15625 ; 6250, 31250
Activity 4: x = 4 ; x = 6 ; x = 5 ; x = 7
Activity 5: 25, 36, 49 ; 26, 37, 50 ; 24, 35, 48 ; 60, 84, 112
Activity 6: 21 ; 18
Activity 7: 8, 13, 21 ; 13, 21, 34
Activity 8: [Student's own answer]
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