PRACTICE GUIDE CITADEL SECURITIES
Citadel Securities Number Sequences Practice Test
Citadel Securities does not publish the shape of its number sequences screen, and candidates describe it as 20 to 30 questions in 10 to 25 minutes, roughly about 30 to 60 seconds per question, answered by typing the number, with no calculator.
Those are ranges across firms running this format rather than Citadel Securities's own figures, so treat them as the shape to train against and check the instruction screen on the day for the marking rule.
Outcry is not affiliated with Citadel Securities and has no access to their assessment content. This guide describes an assessment format that candidates report publicly; the questions here are generated by Outcry and are not Citadel Securities’s own.
What it screens
A market maker quoting across equities, options, fixed income and ETFs globally.
- ✓First and second differences, ratios, and alternating patterns
- ✓Interleaved sequences (two rules taking turns)
- ✓Squares, cubes, primes and factorials recognised on sight
- ✓Committing to an answer with seconds left
Where it sits at Citadel Securities
A market maker quoting across equities, options, fixed income and ETFs globally. What that means for the screen is that the questions tend to be drawn from the work rather than from a textbook, so the format below is the shape to train against rather than a syllabus.
Candidates also report 5 other screens at Citadel Securities, covered separately on this site. Where a firm runs several, they usually sit in one round rather than spread across the process, so the pacing of the whole set matters more than any single section.
The format
Citadel Securities does not publish this screen's shape, and it varies between firms, so these are the ranges candidates report rather than exact figures.
| Questions | 20 to 30 |
|---|---|
| Time | 10 to 25 minutes |
| Per question | about 30 to 60 seconds |
| Negative marking | Varies by firm and year |
| Answer style | Typed next term |
| Where it sits | Usually the same sitting as the arithmetic screen |
What it tests, with a worked example
Every example below is generated by Outcry, drawn from the same question generators the timed drills run. None of them is Citadel Securities’s.
Second-order differences
The differences themselves form a pattern - the give-away for a quadratic rule.
Example
Which one does not belong: 83, 16, 81, 49?
- 81
- 83
- 49
- 16
Answer 83
81, 49, 16 are all perfect squares. 83 is not.
Interleaved sequences
Two rules taking alternate turns, which reads as noise until you split the list.
Example 1
8, 16, 32, 64, 128, ? What comes next?
Answer 256
Each term multiplies by 2, so 128 × 2 = 256.
Example 2
43, 49, 55, 61, 67, ? What comes next?
Answer 73
Each term adds 6, so 67 + 6 = 73.
Example 3
9, 25, 57, 121, 249, ? What comes next?
Answer 505
Double and add 7: 249 × 2 + 7 = 505.
Named number families
Squares, cubes, primes, factorials and Fibonacci, recognised rather than derived.
Example 1
4, 14, 54, 214, 854, 3414, ?
Answer 13654
Each term is 4 times the last, minus 2. 4 × 3414 − 2 = 13654.
Example 2
6, 3, 18, 9, 54, 27, ?
Answer 162
Two sequences interleaved, both multiplying by 3. Positions 1, 3 and 5 run 6, 18, 54, so the next is 162.
Example 3
34, 38, 46, 58, 62, 74, ?
Answer 82
These are twice each prime, starting at 17. The gaps do not settle, which is the hint. The next prime after 37 is 41, so the answer is 82.
Operation chains
Each term built from the last by a repeating operation cycle rather than one rule.
Example 1
10, 15, 23, 34, 48, ? What comes next?
Answer 65
The gaps are 5, 8, 11, 14, growing by 3. Next gap 17: 48 + 17 = 65.
Example 2
11, 13, 17, 19, 23, ? What comes next?
Answer 29
Consecutive primes from 11. After 23 comes 29.
Example 3
1, 8, 27, 64, 125, ? What comes next?
Answer 216
Cubes from 1³. Next is 6³ = 216.
Position-dependent rules
The rule uses the index rather than the previous term, so differences never settle.
Example 1
How many numbers from 1 to 150 are divisible by 3 or by 5?
Answer 70
50 multiples of 3, 30 of 5, and 10 counted twice as multiples of 15: 50 + 30 − 10 = 70.
Example 2
What comes next: 1, 8, 27, 64, 125, ?
Answer 216
Cubes from 1: next is 6³ = 216.
Example 3
What comes next: 15, 21, 28, 36, 45, ?
Answer 55
Triangular numbers - the gaps go up by one each time. Next is 45 + 10 = 55.
Sequences with a planted decoy
An opening that fits two rules, where the fourth term is what decides between them.
Example 1
6, 3, 18, 9, 54, 27, ?
Answer 162
Two sequences interleaved, both multiplying by 3. Positions 1, 3 and 5 run 6, 18, 54, so the next is 162.
Example 2
34, 38, 46, 58, 62, 74, ?
Answer 82
These are twice each prime, starting at 17. The gaps do not settle, which is the hint. The next prime after 37 is 41, so the answer is 82.
Example 3
9, 12, 18, 27, 39, 54, ?
Answer 72
The gaps are 3, 6, 9, 12, 15 - each one 3 bigger than the last. The next gap is 18, so 54 + 18 = 72.
What a good score looks like
These are usually scored alongside the arithmetic section rather than reported separately, so a standalone cutoff is rarely visible. Candidates describe the sequences round as the one that responds fastest to practice, because the rule families are few.
How to train for it
- 01Learn to take first and second differences automatically, before trying anything cleverer. It resolves most items on its own.
- 02Practise splitting a list into odd and even positions the moment the differences look random. That one move solves every interleaved item.
- 03Check the rule against the last term before you answer. A rule that fits the first three and fails the fourth is the most common way to lose one of these.
TRAIN IT HERE
The drills that match each section
Sequence Sprint
Timed next-term sequences, exactly the assessment format.
Arithmetic Drill
The raw calculation speed that sequence tests assume you already have.
SIT THE FULL BATTERY
All the sections back to back on one clock, marked the way the real screen marks them, with a by-skill breakdown at the end. Included with any pass.
Also reported at Citadel Securities
Common questions
- Is the Citadel Securities number sequences test multiple choice?
- Reported as typed next term. Formats move, so treat this as the shape rather than a guarantee.
- How long is the Citadel Securities number sequences test?
- Candidates report 20 to 30 questions in 10 to 25 minutes, roughly about 30 to 60 seconds per question.
- Is there negative marking on the Citadel Securities number sequences test?
- It varies by firm and by year. Where a paper does mark negatively, skipping beats guessing; where it does not, answer everything. Check the instruction screen before you start - it is always stated there.
- How do I practise for it free?
- Every drill linked on this page is free to play, with no account, inside a daily run cap. Questions are generated fresh each run, so there is nothing to memorise between attempts.