How to solve number series questions
The number-series decision ladder
Every number series yields to an ordered sequence of checks. Climb the ladder instead of staring, and the rule reveals itself in under a minute.
Updated
Number series feel like inspiration but are pure procedure. Test-prep tradition has converged on a decision ladder: an ordered list of rule families to test, cheapest first. Run it top to bottom and you will find the rule — or know quickly that the item uses a rarer pattern.
Rungs 1–3: differences, ratios, second differences
1) Write the differences between neighbors. Constant? Arithmetic series — done. 2) Not constant? Check ratios: is each term a fixed multiple of the last? 3) Check the differences of the differences: a constant second difference means the gaps themselves grow steadily (+2, +5, +8…).
Rungs 4–5: alternation and interleaving
4) Do operations alternate (+3, ×2, +3, ×2)? The differences will zigzag. 5) Split the series into odd and even positions and test each half separately — interleaved series are two easy patterns braided together, and they explain most 'impossible' items.
Rungs 6–9: known families
6) Big accelerating jumps? Compare against squares (1, 4, 9, 16…) and cubes with an offset. 7) Check primes (2, 3, 5, 7, 11…) with an offset. 8) Check Fibonacci-style: is each term the sum of the previous two? 9) Last resort: digit-level rules — e.g., each term plus the sum of its own digits.
The strategy
- Always write the differences first. Ten seconds, and it decides rungs 1–4 at a glance.
- Verify your rule against every given term — a rule that fits four of five terms is not the rule.
- Predict the next term, then find it among the options — don't reverse-engineer from the options.
- The 'repeat the last step' answer is the most common trap: it's what the series would do if the pattern stopped evolving.
Common traps
- Applying the last visible difference once more when the differences are accelerating.
- Missing interleaving: if the sequence rises and falls, split odd/even positions immediately.
- Arithmetic slips under time pressure — the options include your miscalculation.
Speed · ~45s/item: Budget 25–70 seconds by difficulty. The ladder's power is that easy rules are eliminated in seconds, so hard items get your remaining time.
Try it yourself: 4 practice questions
Pick an answer, then reveal it. Nothing is recorded, there is no clock, and none of these questions is ever used in a test.
What comes next in the series?
Reveal the answer
The answer is E — 22.
Show why — the worked reasoning
What comes next in the series?
Reveal the answer
The answer is E — 52.
Show why — the worked reasoning
What comes next in the series?
Reveal the answer
The answer is A — 47.
Show why — the worked reasoning
What comes next in the series?
Reveal the answer
The answer is C — 59.
Show why — the worked reasoning
Try questions like this
The free test has 20 questions across abstract, numerical, verbal and spatial reasoning. It takes 12 minutes, needs no sign-up, and explains every answer.
A free account opens every lesson, practice drills and a study plan built from your results.
Questions people ask
What is the first thing to check in a number series?
The differences between neighbouring numbers. If they are constant, it is a plain arithmetic series. If not, check ratios, then the differences of the differences.
What if the numbers go up and down?
Split the series into odd and even positions. Two simple series interleaved, or two operations that alternate, are the most common causes.
How long should a number series take?
About 25 to 70 seconds, depending on difficulty. Easy rules are ruled out in seconds when you check them in a fixed order.
Will number series questions be on the free test?
Maybe. The free test gives numerical reasoning 5 of its 20 questions, spread across 13 different question types, so any one test may or may not include this kind.