Understand the idea.
Look at the change
A number sequence lists numbers in order using a rule. A constant-step rule adds or subtracts the same amount between neighbouring numbers. The starting number and the step are both needed to reproduce the sequence.
Compare each pair of neighbours. In , the changes are all add four. Checking several changes helps you see whether a suggested constant step fits every number that is shown.
Work in both directions
Apply a given rule once for each move to the next number. Starting at and subtracting gives , then , then . Count the starting value as the first number when listing terms.
A missing middle number must fit both neighbours. With an add-five rule, needs : it is five after ten and five before twenty. Checking both sides can catch a skipped step.
| Position | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Number | 3 | 7 | 11 | 15 | 19 |
See the method in action.
A growing sequence
Start at 6 and add 4 each time. Write the first 4 numbers.
Worked solution
- 1
Record the starting number as the first number.
No addition is needed before the first listed number.
- 2
Apply the rule for the second and third numbers.
Each move adds the same four.
- 3
Find the fourth number.
Three moves from the start produce four numbers: six, ten, fourteen and eighteen.
6, 10, 14, 18.
A missing number
The rule is subtract 3. Complete 22, 19, __, 13.
Worked solution
- 1
Check the rule on the first shown move.
The given neighbours follow the subtract-three rule.
- 2
Find the missing next number.
Use the same subtraction on the current number.
- 3
Check against the following number.
The missing sixteen fits the rule on both sides.
16.
Try it yourself.
Check your understanding
The rule is add 6. What follows 2, 8, 14?
Show answer & reasoning
20.
The given rule adds six each time. Both and fit it; the next number is .
Keep practising
6 worksheet questions
Read the questions online
- Start at 3 and add 3 each time. Write 5 numbers.
- Start at 18 and subtract 2 each time. Write 4 numbers.
- The rule is add 5. Fill the gap: .
- The sequence has a constant step. Describe it.
- The rule is add 3. Correct the error: .
- A child saves 4 stickers each day. The total after day 1 is 4. Give the totals after days .
Read the worked solutions
- Start at 3 and add 3 each time. Write 5 numbers.
Add 3 four times after the starting number.
. - Start at 18 and subtract 2 each time. Write 4 numbers.
Subtract 2 from each previous number.
. - The rule is add 5. Fill the gap: .
and .
17. - The sequence has a constant step. Describe it.
Each pair of neighbours differs by 4.
Add 4 each time. - The rule is add 3. Correct the error: .
and .
16 should be 15. - A child saves 4 stickers each day. The total after day 1 is 4. Give the totals after days .
Add 4 for each extra day.
stickers.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Number sequences; step-by-step rules; decisions; explaining resulting patterns.
Official curriculum source ↗