Take the differences. Then take them again.
1, 3, 6, 10, ... and a candidate stares at it hoping the rule will announce itself. It will not. But the gaps between those numbers are 2, 3, 4 — and the gaps between _those_ are 1, 1, 1. The rule was two mechanical steps away the whole time. This is not a trick; it is nearly the whole of sequence questions, and it works when inspiration does not.
The differences method
Write the sequence. Underneath, write the gaps. If the gaps are constant, the rule is linear and you are done: keep adding the gap.
If the gaps are not constant, write the gaps of the gaps. If those are constant, the rule is quadratic — the sequence is growing at a growing rate — and you can extend it by working back up: extend the bottom row, use it to extend the middle row, use that to extend the top.
1, 3, 6, 10, 15, 21. Gaps: 2, 3, 4, 5, 6. Gaps of gaps: 1, 1, 1, 1. Constant, so the next gap is 7 and the next term is 28. You never needed to recognise triangular numbers, though it helps to know them.
The reason to drill this is that it is mechanical. It does not require you to be clever at the moment you are least able to be — under a clock, on a question you have never seen. Mechanical beats inspired when the clock is running.
When it is not differences, it is one of four things
If the differences do not resolve after two rows, stop taking them and check the short list instead. Almost everything else is:
Ratios. Divide instead of subtracting. 3, 6, 12, 24 has constant differences of nothing useful but a constant ratio of 2.
Two interleaved sequences. 2, 100, 4, 90, 8, 80 is not one sequence; it is two, alternating. This is the commonest disguise, and the tell is a sequence that jumps around wildly — a single rule rarely oscillates.
Operations on the previous terms. Each term is the sum of the two before it, or the previous term times its position.
A rule about the digits, not the values — sums of digits, reversals. Rarer, and worth checking last.
Run that list rather than staring. Same principle as pattern completion: you are testing a hypothesis, not waiting for a revelation.
Verify on three, and mind the direction
Two habits that cost seconds and save marks.
Verify across three terms, never two. Any two numbers support infinitely many rules. 2 then 4 could be plus-two, times-two, or squares. Three terms usually pin it; two never do. This is the same discipline as verifying a visual pattern across three figures, and it fails in the same way — candidates commit to a rule the third term would have disproved.
Check what is being asked. Sequence questions ask for the next term, or the missing middle one, or the tenth one, or the sum. Finding the rule and then answering the wrong question is a real and common way to lose a mark you had earned. Reread the stem after you have the rule, not before.
And if the tenth term is wanted, do not extend the sequence ten times by hand under a 108-second clock. Find the closed form if it is quick, and if it is not, the question probably did not want the tenth term of a hard sequence — reread it.
The rules behind this
Sourced to the official brochure rather than restated here, so there is one place to correct when the Council revises it.
Part B examines six named areas: Visual Reasoning, Logical Derivation, General Knowledge/Architecture and Design, Language Interpretation, Design Sensitivity and Thinking, and Numerical Ability.
Visual Reasoning — understanding and reconstructing 2D and 3D composition. Logical Derivation — decoding a situation or context and drawing conclusions. General Knowledge, Architecture and Design — current issues, important buildings, historical progression, innovation in materials and construction. Language Interpretation — meaning of words and sentences, English grammar. Design Sensitivity and Thinking — observing and analysing people, space, product, environment; semantics, metaphor, problem identification. Numerical Ability — basic mathematics and its association with creative thinking; unfolding space using geometry.
Source · verified 2026-07-16
Part B allows 108 seconds per question, presented one after another, on an adaptive engine.
90 minutes across 50 questions. The adaptive structure dates to NATA 2025 per the President's foreword in V2.0, which states that NATA 2026 continues it.
Source · verified 2026-07-16
What almost everyone believes
“If I look at the sequence long enough, I will spot the pattern.”
Take the differences. It is mechanical, it works when inspiration does not, and it does not require you to be clever under a clock.
Sequences feel like they should yield to insight, so candidates give them attention and burn ninety seconds. But the rule is a specific transformation, and you either test for it or you do not. Two rows of differences resolve most sequences outright and cost about ten seconds. The value of a mechanical method is precisely that it works at the moment you are least able to be inspired — under time, on a question you have never seen, with no way back.
Depending on how long you have
Foundation
Understand the skill. Months out, or starting from zero.
Learn the differences method until it is a reflex you run before thinking, and learn the common families by sight: squares, cubes, triangular numbers, Fibonacci, powers of two. Recognition is instant and derivation is not; the drill converts one into the other over weeks.
Drill
The practice protocol. What to repeat, how often, how to score it.
Differences first, always, before staring. If two rows do not resolve it, run the short list: ratios, interleaved, operations, digits. Verify across three terms. Then reread the stem to check which term was actually wanted — and track how often you nearly answered the wrong question.
Exam-Day
What to actually do under the constraint — 108 seconds, no instruments, one pass.
Do not wait for the rule to appear. Write the gaps, then the gaps of the gaps. If nothing resolves in two rows, check for two interleaved sequences — the tell is wild oscillation. Verify on three. And if you are at sixty seconds with no rule, eliminate and commit.
Try it
Ten minutes. Run the method rather than looking.
- 01For each: 2, 5, 10, 17 — 1, 4, 9, 16 — 3, 6, 12, 24 — 1, 1, 2, 3, 5 — 5, 100, 10, 90, 20, 80.
- 02Do NOT stare. Write the sequence, write the gaps underneath, and if needed the gaps of the gaps.
- 03Note which ones the differences cracked and which needed the short list. (The last one is two interleaved sequences — the oscillation is the tell.)
- 04Verify every rule across three terms before accepting it.
- 05Time yourself. Under twenty seconds each is the target, and the method is what gets you there — not familiarity.
The short version
Take the differences; if they do not resolve, take the differences of the differences. Constant first row means linear, constant second row means quadratic, and you extend by working back up. If two rows fail, run the short list — ratios, interleaved, operations on previous terms, digits — with interleaving being the commonest disguise and wild oscillation its tell. Verify across three terms, never two. Then reread the stem, because finding the rule and answering the wrong question is a real way to lose a mark you had earned.
Next: deduction — and the discipline of not concluding more than you were given.
Questions people actually ask
- How do I find the rule in a number series?
- Take the differences between consecutive terms. If those are constant the rule is linear. If not, take the differences of the differences — if those are constant the rule is quadratic and you extend by working back up. Two rows resolve most sequences in about ten seconds, without needing to recognise anything.
- What if the differences method does not work?
- Check four things: ratios (divide instead of subtracting), two interleaved sequences (the tell is wild oscillation — a single rule rarely jumps around), operations on previous terms like Fibonacci, and rules about the digits rather than the values. Interleaving is the commonest disguise.
- How many terms should I check before accepting a rule?
- Three, never two. Any two numbers support infinitely many rules — 2 then 4 could be plus-two, times-two, or squares. Three usually pins it. Candidates lose marks by committing to a rule the third term would have disproved.