Write the gaps under the list, then test the rule on every number before choosing.
Practice test 1 is free. No card needed.
Number patterns hide a rule in a list; your child finds it by writing the gaps and testing every number. A child in Year 7 now sits Quantitative Reasoning in Year 8, in June 2027 Expected.
Checked by the SelectiveReady team on 12 October 2026 · Updated 27 October 2026 · How we check facts
Independent. Not affiliated with the Victorian Department of Education or ACER.
It's a list that grows or shrinks by a hidden rule, and your child has to find the rule before using it. ACER says Quantitative Reasoning tests thinking and reasoning with numbers, patterns and shapes, and a sequence is that skill in its plainest form.
These three are our own, from easier to harder. Each one shows the answer and the working. For each wrong option, write the gaps under the list together and find the first number where its rule stops fitting.
What is the next number in this sequence?
2, 6, 7, 21, 22, 66, ?
Answer: A
Answer: A
The rule switches between two steps: multiply by 3, then add 1 (2 → 6 → 7 → 21 → 22 → 66). The last step was × 3, so the next step is + 1, giving 67. Choosing 198 repeats the × 3 step instead of switching.
What are the next two numbers in this sequence?
20, 1, 17, 2, 14, 4, 11, 8, ?, ?
Answer: D
Answer: D
Two patterns are woven together. Every other number, starting with 20, goes down by 3: 20, 17, 14, 11, so the next is 8. The numbers in between double: 1, 2, 4, 8, so the next is 16. The 9th number belongs to the first pattern, so the order is 8 then 16, not 16 then 8.
This sequence continues in the same way.
1, 2, 4, 7, 11, 16, …
What is the 20th number in the sequence?
Answer: B
Answer: B
The gaps are 1, 2, 3, 4, 5, so the 20th number is 1 plus 19 gaps: 1 + (1 + 2 + … + 19). Pair the gaps (1 + 19, 2 + 18, …): nine pairs of 20 plus the middle 10 make 190. Adding the starting 1 gives 191. Choosing 190 forgets the starting 1; 211 adds one gap too many.
Work through the same checks in order, from the simplest kind of rule to the trickiest. The order matters because it stops your child settling on a rule that fits only the first few numbers. Quantitative Reasoning shares 60 minutes with Mathematics, so a routine that takes seconds is worth having.
There is no calculator in the exam room, so the working stays small and written down. This is our method, not ACER's.
Write the difference between each pair of neighbours under the list. Steady or growing gaps show up at once.
If the gaps make no sense, try multiplying, or steps that take turns, such as × 3 then + 1.
Read every other number on its own. A hard-looking list can be a pair of simple patterns woven together.
A rule that fits the first few numbers but not the last is the wrong rule.
The next number, the next pair, or one far along such as the 20th? Check the position and the order before choosing.
Each wrong option in our questions is the answer a particular slip gives. Ask which option looked right at first, find it below and name the slip together. Then make up a fresh pattern that sets the same trap and see if your child spots it.
Pattern spotting needs no special books, just a habit of saying the rule out loud. ACER says these skills grow over time, through a culture of learning, varied engaging material and talking freely about ideas, so plan a few short games a week rather than one long session.
For more of this kind, see our quantitative reasoning sample questions. Three questions show the method; a full sitting shows whether your child can still use it with Mathematics on the same clock. Our selective entry practice tests follow the real timing, Practice test 1 is free, and the results by skill show whether patterns cost marks.
Practice test 1 marks every answer and shows results by skill: what your child already does well and the three skills to work on next.
Practise for the real test
Practice test 1 is free. Then packs from A$109 for 12 months, or A$9 a week, per exam.