The idea, step by step
Look at each jump
A sequence follows a rule. Read it from left to right and compare neighbouring terms. In 7, 12, 17, 22, each term is 5 more than the one before it. The rule is add 5 each time. Check every jump, not only the first.
An additive rule changes the number by the same amount. Subtraction is also an additive change: 36, 30, 24, 18 subtracts 6 each time. Include the starting number when explaining a pattern.
Compare adding with multiplying
In 3, 6, 12, 24, the jumps are 3, 6 and 12, so the rule is not add 3. Each term is twice the previous term. This is a multiplicative rule: multiply by 2.
A short list can have more than one possible rule. Here we look for a simple rule that fits every given term. Name the operation, then test it on each neighbouring pair.
A common trap
I saw 3 followed by 6, so I used add 3 for 3, 6, 12, 24.
Instead: Check all jumps. Adding 3 would give 3, 6, 9, 12. The given sequence doubles.
See the thinking
Continue an additive pattern
The rule is subtract 7. Start at 50. Write five terms.
- The starting number, 50, is the first term.
- Subtract 7 repeatedly: 50 − 7 = 43, 43 − 7 = 36, 36 − 7 = 29, 29 − 7 = 22.
- Count five terms including the starting number.
Check the type of rule
Describe a simple rule for 4, 12, 36, 108. Find the next term.
- The differences are 8, 24 and 72; they are not equal.
- Check multiplication: 4 × 3 = 12, 12 × 3 = 36 and 36 × 3 = 108.
- Apply the same rule: 108 × 3 = 324.
Check your understanding
The rule is add 8. What follows 11, 19, 27?
Show answer
35
27 + 8 = 35; both earlier jumps also add 8.
Your turn
6 questions · 11 marks · Work at your own pace.
Read the questions online
- Continue 9, 15, 21, 27 with two more terms, using a constant addition rule.2 marks
- Start at 48 and halve each time. Write the first five terms.2 marks
- Fill the gap in 5, 10, __, 40, 80. Use a multiply-by-2 rule.1 mark
- Does add 4 fit every jump in 6, 10, 14, 19? Explain.2 marks
- A club saves 6 dollars each week. It has 13 dollars now. How much will it have after three more weeks?2 marks
- Create four terms starting at 7 using a multiply-by-3 rule.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Continue 9, 15, 21, 27 with two more terms, using a constant addition rule.2 marks
Each jump adds 6.
27 + 6 = 33; 33 + 6 = 39.
33, 39 - Start at 48 and halve each time. Write the first five terms.2 marks
Include the starting number.
Divide by 2 four times.
48, 24, 12, 6, 3 - Fill the gap in 5, 10, __, 40, 80. Use a multiply-by-2 rule.1 mark
10 × 2 = 20.
20 × 2 = 40.
20 - Does add 4 fit every jump in 6, 10, 14, 19? Explain.2 marks
10 − 6 = 4 and 14 − 10 = 4.
19 − 14 = 5, so add 4 does not fit all terms.
No. The last jump adds 5. - A club saves 6 dollars each week. It has 13 dollars now. How much will it have after three more weeks?2 marks
Three weeks add 3 × 6 = 18 dollars.
13 + 18 = 31 dollars.
31 dollars - Create four terms starting at 7 using a multiply-by-3 rule.2 marks
7 × 3 = 21; 21 × 3 = 63; 63 × 3 = 189.
7, 21, 63, 189
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics 2026
Additive/multiplicative rules; steps/decisions; predicting and explaining patterns.
Official curriculum source ↗