Look for the constant difference
In 5, 8, 11, 14, each term is 3 more than the previous one.
Check the gap between neighbouring terms before deciding the rule.
Year 7
Generate and explain sequences
Continue sequences accurately, describe the rule clearly, and use pattern structure to find missing terms.
Lesson overview
Algebra - patterns and sequences
A sequence follows a rule. Some rules tell us how to move from one term to the next, such as add 4 each time. Others describe how the position of a term connects to its value. In Year 7, we focus on spotting the pattern clearly, continuing it correctly and explaining the rule in words.
A sequence can go down as well as up
In 20, 17, 14, 11, the rule is subtract 3 each time.
Negative change still follows a pattern.
Missing terms must fit the same rule
If the sequence is 4, 7, 10, __, 16, then the missing term must be 13.
The same step size must work all the way across the sequence.
Worked example
Find the next two terms in the sequence 6, 10, 14, 18.
| Terms | Difference |
|---|---|
| 6 to 10 | +4 |
| 10 to 14 | +4 |
| 14 to 18 | +4 |
- Compare each pair of neighbouring terms.
- Notice the difference is always +4.
- Add 4 to 18 to get 22.
- Add 4 again to get 26.
Try it
Find the rule first, then use it consistently across the sequence.
Question 1
What is the next term in 5, 8, 11, 14, ...?
Question 2
Which rule describes 9, 15, 21, 27, ...?
Question 3
What is the missing term in 4, 7, 10, __, 16?
Question 4
What is the next term in 20, 17, 14, 11, ...?
Question 5
Which statement is correct about the sequence 6, 10, 14, 18, ...?
| From | To | Change |
|---|---|---|
| 6 | 10 | +4 |
| 10 | 14 | +4 |
Common mistakes
Watch for these when working through the lesson.
- Using a different step size later in the same sequence.
- Looking only at the first two terms and not checking the rest.
- Forgetting that a sequence can decrease.
Related topics
These ideas fit closely with this lesson.
- Simplify linear expressions.
- Substitute into formulae.
- Operations with negative numbers.