How to solve: Numerical Sequences
What this category tests
Measures inductive reasoning — spotting the hidden rule behind a list of numbers from just a handful of examples, then correctly predicting the next term.
Where this typology comes from
Number- and letter-series items trace back to the first mass-administered intelligence tests. Psychologist Arthur Otis (a student of Lewis Terman) designed an early group-administered, multiple-choice test around 1917-18 whose item formats fed directly into the U.S. Army Alpha test, used to screen 1.7 million WWI recruits.
How to approach it
Compute the differences between consecutive terms first; if those aren't constant, take the differences of the differences (second differences) or check ratios instead. Watch for sequences that interleave two simpler patterns at alternating positions. Always confirm your rule reproduces every given term, not just the last couple, before extrapolating.
Worked example
What number comes next in this sequence?
2, 5, 10, 17, 26, ?
- 35
- 36
- 37 ✓ Correct answer
- 39
Explanation The differences between consecutive terms are 3, 5, 7, 9 — each one 2 more than the last. Following that pattern, the next difference should be 11, so the next term is 26 + 11 = 37. (In fact each term equals n² + 1: 1²+1=2, 2²+1=5, 3²+1=10, and so on.)
Practice Numerical Sequences
- Numerical Sequences I · 12 questions · Difficulty 2 out of 5
- Numerical Sequences II — Letter Sequences · 12 questions · Difficulty 3 out of 5
- Numerical Sequences III — Numerical Analogies · 12 questions · Difficulty 3 out of 5
Guides that include this category
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- Numerical reasoning: the formats of a hiring test and how to practice