Count on by a constant step
4, 7, 10, 13 increases by 3 each time.
The difference stays the same.
Year 6
Generate and describe linear number sequences
Spot the constant step in a sequence and describe the rule clearly.
Lesson overview
Algebra
A linear sequence changes by the same amount each time. We can generate more terms by keeping the same step and describe the sequence by stating its rule.
Count back by a constant step
20, 16, 12, 8 decreases by 4 each time.
Linear sequences can go backwards too.
Worked example
Continue 5, 9, 13, 17, ...
| Term | Difference |
|---|---|
| 5 to 9 | +4 |
| 9 to 13 | +4 |
| 13 to 17 | +4 |
- Find the difference between terms.
- The difference is +4 each time.
- Add 4 to 17.
- The next term is 21.
Try it
Check the difference between terms before deciding the rule.
Question 1
What comes next: 4, 7, 10, 13, ... ?
Question 2
What is the rule for 20, 16, 12, 8, ... ?
Question 3
Which is a linear sequence?
3,6,9,12
2,4,8,16
1,3,6,10
Question 4
What comes next: 5, 9, 13, 17, ... ?
Question 5
Which rule matches 2, 5, 8, 11?
| 2 to 5 | 5 to 8 | 8 to 11 |
|---|---|---|
| +3 | +3 | +3 |
Common mistakes
Watch for these when working through the lesson.
- Using a changing step by mistake.
- Only checking one pair of terms and not the whole sequence.
- Mixing up an increasing rule and a decreasing rule.
Related topics
These ideas fit closely with this lesson.
- Use simple formulae.
- Express missing number problems algebraically.