Alongside mental arithmetic, several trading firms — Optiver is the best-known — include a timed number-sequence test: you are shown a sequence and must supply the next or missing term, fast. It measures pattern recognition and working speed under pressure, not advanced maths.
The common pattern types
Most interview sequences are built from a small toolkit:
| Pattern | Example | The tell |
|---|---|---|
| Arithmetic | 3, 7, 11, 15, … | Constant first difference (+4) |
| Geometric | 2, 6, 18, 54, … | Constant ratio (×3) |
| Second-order | 1, 2, 4, 7, 11, … | Differences form a pattern (1, 2, 3, 4) |
| Interleaved | 1, 10, 2, 20, 3, … | Two sequences woven together |
| Neighbour ops | 1, 1, 2, 3, 5, 8, … | Each term combines previous ones (Fibonacci) |
| Position-based | 1, 4, 9, 16, … | Term n is a function of n (here n²) |
A systematic approach
Under time pressure, run the same checklist every time:
The checklist. 1) First differences — subtract consecutive terms; constant means arithmetic, a clean pattern means second-order. 2) Ratios — divide consecutive terms; constant means geometric. 3) Alternation — if values zig-zag, split into odd- and even-indexed subsequences and analyse each. 4) Index relationship — compare each term to its position, so squares, cubes, and n-based formulas jump out.
Running this beats staring at the numbers hoping the rule appears, and the first two checks catch the large majority of cases.
Why it's pure practice
Speed comes from recognising which check to reach for first — and that is entirely a matter of reps. The patterns are few; with enough exposure your eye starts to see "constant difference" or "interleaved" before you consciously test for it.
Practise the format
NeetQuant's Sequences simulator drills exactly this — spot the rule, type the next term, against the clock — and pairs with the Mental Math Blitz for the arithmetic speed these tests also demand. See the speed mental-math guide for the broader assessment context.