Number Sequence Tests in Trading Interviews: The 8 Pattern Types & How to Practice

A taxonomy of every pattern the tests actually use, one worked example with the full math, and the traps that burn most candidates.

Updated July 3, 2026 · QuantVault

Why trading firms use sequence tests

Arithmetic screens like Optiver’s 80-in-8 measure raw calculation speed. Sequence tests measure something different: how fast you generate hypotheses, test them against evidence, and discard the wrong ones. That loop — propose a pattern, check it against every data point, revise — is a miniature version of what a trader does when a market moves and they need to figure out why. Firms that lean on sequence-style pattern tests include IMC (candidates call its screen the “24-in-18” — roughly 24 sequences in 18 minutes), Akuna, Maven, and Flow Traders. The format details vary by firm and cycle, so check the specific guides: IMC’s online assessment, Akuna’s, Flow Traders’, and the Maven interview guide.

The good news: unlike brainteasers, sequence tests draw from a small, learnable taxonomy. In our experience nearly every question is one of eight types, or a light disguise of one.

The 8 pattern types

#	Type	Detection cue	Example
1	Arithmetic	Constant first difference	$7, 12, 17, 22 \to +5$
2	Geometric	Constant ratio	$3, 6, 12, 24 \to \times 2$
3	Second-order (quadratic)	Differences form an arithmetic sequence	$2, 6, 12, 20, 30 \to n(n+1)$
4	Affine recursion	Roughly doubling/tripling, but ratio drifts	$4, 9, 19, 39 \to a_{n+1}=2a_n+1$
5	Interleaved	No sense read straight; odd/even positions work separately	$1, 10, 3, 8, 5, 6 \to$ odds $+2$, evens $-2$
6	Alternating operations	Growth alternates small/large	$2, 4, 12, 14, 42 \to +2, \times 3$ repeating
7	Reference sequences	Terms sit near squares, cubes, primes, factorials, Fibonacci	$0, 3, 8, 15, 24 \to n^2 - 1$
8	Digit tricks	Nothing numeric works; look at the digits themselves	$1, 11, 21, 1211 \to$ look-and-say

Types 1–4 cover the majority of questions on every test we’ve seen candidates report. Types 5–8 are where the hard back-third of a test lives.

The core tool: the differences method

Almost every non-digit pattern yields to one algorithm: take differences (or ratios) repeatedly until you hit something you recognize, then propagate back up. Here is a full worked example.

Problem: $4, \; 9, \; 19, \; 39, \; 79, \; ?$

Step 1 — first differences.

$$5, \; 10, \; 20, \; 40$$

Step 2 — recognize the layer. The differences are geometric with ratio $2$, so the next difference is $80$, giving $79 + 80 = \mathbf{159}$. Under time pressure, you stop here — that’s the answer.

Step 3 — the deeper structure (worth knowing for follow-ups). Geometric differences are the fingerprint of an affine recursion. Guess $a_{n+1} = 2a_n + c$: from $4 \to 9$ we get $c = 1$, and $2(9)+1 = 19$, $2(19)+1=39$ confirm it. To get a closed form, shift by the fixed point of the map ($x = 2x+1 \Rightarrow x = -1$), i.e. let $b_n = a_n + 1$:

$$b_{n+1} = 2b_n, \quad b_1 = 5 \;\;\Rightarrow\;\; b_n = 5 \cdot 2^{n-1} \;\;\Rightarrow\;\; a_n = 5 \cdot 2^{n-1} - 1$$

Check: $a_6 = 5 \cdot 32 - 1 = 159$. Matches Step 2. This fixed-point shift is the same trick that solves gambler’s ruin-style recurrences, so it pays off twice.

A decision order that saves seconds

Scan magnitude growth: roughly linear → try differences (types 1, 3); roughly exponential → try ratios, then affine recursion (types 2, 4).
If neither, split odd and even positions (type 5) — this alone rescues a huge fraction of “weird” sequences.
Then check distance to squares, cubes, primes, Fibonacci (type 7).
Only then consider digit games (type 8). They’re rare and cheap to spot late.

The traps

Confirming on two terms. A hypothesis that fits three consecutive terms can still fail the fourth. Always verify against every given term before answering — test writers deliberately plant sequences whose first few terms fit a simpler wrong rule.
Anchoring. If your first idea fails one term, drop it completely rather than patching it. Circular tweaking is the main way candidates lose 90 seconds on one question.
Over-engineering. With five or six given terms, the intended rule is almost never a cubic. Simple first.
Refusing to skip. These tests are scored on totals. A question that resists 40 seconds of the decision order above should be flagged and abandoned; the marginal question you gain at the end is worth more.

How to practice

Two weeks of 20-minute daily drills is usually enough, because the skill is recognition, not computation. Drill each pattern type in isolation until detection is instant, then move to mixed timed sets so the classification step itself gets fast. Keep an error log by pattern type — most people discover they specifically miss interleaved and alternating-operation sequences, which is fixable in days once named. Round it out with adjacent formats: the pattern-recognition sections of firm OAs often sit next to brainteaser and probability sections, so don’t train sequences in a vacuum.

Ready to drill? Work through timed sets in the QuantVault problem bank, run the firm-specific formats in the IMC OA guide, and sharpen the speed side with our trading games.

Frequently asked questions

What is the IMC 24-in-18 sequence test?

It is the candidate nickname for IMC's number sequence screen: roughly 24 sequence questions in 18 minutes, so about 45 seconds per question. The questions get harder as you progress, so banking time on the early arithmetic and geometric patterns is the standard strategy. Exact counts and timing vary by region and recruiting cycle, so treat the format as approximate.

How is a sequence test different from Zetamac-style mental math?

Mental math screens like Optiver's 80-in-8 test calculation speed on arithmetic you already know how to do. Sequence tests measure hypothesis generation: proposing a candidate pattern, checking it against every given term, and discarding it fast when it fails. You should train them separately, because being fast at one does not transfer automatically to the other.

What order should I try patterns in during the test?

Check growth first: near-linear growth points to differences (arithmetic or quadratic), near-exponential growth points to ratios or an affine recursion like a(n+1) = 2a(n) + 1. If neither works, split the sequence into odd and even positions to test for interleaving, then compare terms against squares, cubes, primes, and Fibonacci. Digit-based tricks are rare, so save them for last.

How long does it take to prepare for a number sequence test?

For most candidates, two weeks of short daily drills is enough, because the underlying taxonomy is only about eight pattern types. Drill each type in isolation until recognition is instant, then switch to mixed timed sets that force you to classify under pressure. Keeping an error log by pattern type is the fastest way to find and fix your specific blind spots.

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