Mastering Sequence Problems: The Definitive Guide to Pattern Recognition in Trading Interviews

Sequence questions can vary widely in complexity, but most are based on a few common pattern types. Familiarizing yourself with these will help you quickly recognize what kind of logic is at play:

Arithmetic Sequences
Each term increases or decreases by a constant difference. For example, adding +3 each time (\(5, 8, 11, 14, …\)) is a simple arithmetic pattern. Sometimes the difference itself might change in a simple way (e.g. increasing differences).

Geometric Sequences
Each term is multiplied or divided by a constant factor. For instance, multiplying by 2 each step (\(3, 6, 12, 24, …\)) is a geometric sequence.

Fibonacci & Additive Sequences
The next term is the sum (or difference) of previous terms. The classic Fibonacci (\( 1, 1, 2, 3, 5, 8, … \)) adds the last two terms, but variations might add the last three, etc.

Special Number Series
These include patterns based on squares (\( 1, 4, 9, 16, …\)), cubes, prime numbers, factorials, or other mathematical sequences. For example, a sequence might alternate a prime number, then a square number, and so on.

Alternating or Interwoven Sequences
A tricky category where two (or more) interleaved patterns form one sequence. For example, in a sequence like \( 2, 10, 4, 8, 6, 6, …,\) one subsequence (every other term) might be going 2 → 4 → 6 (adding +2) while the alternate terms go 10 → 8 → 6 (subtracting -2). In trading assessments, you might encounter sequences that hide two sequences in one, so always check if the terms alternate following different rules.

Letter Sequences
Instead of numbers, you may see letters or a mix of letters and numbers. These follow alphabetical patterns (e.g. skipping letters, A, C, F, J, …) or other logical progressions with letters. Often you can convert letters to their alphabetical positions (A=1, B=2, etc.) to reveal a hidden numerical pattern, such as “add 3 each time” or “alternate +1, +2, +3, …”.

Not all letter sequences are purely alphabetical, though. Some are based on real-world ordered lists, for example:

• Musical notes: \( D, R, M, F, S, L, T \) (from Do, Re, Mi, Fa, So, La, Ti, …)
• Ordinals: \( F, S, T, F, F, S, S \) (First, Second, Third, Fourth, Fifth, Sixth, Seventh)
• Planets: \( M, V, E, M, J, S, U, N \) (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune)

You might also encounter patterns based on days of the week, months, or other familiar sequences. The Flow Traders sequence test, for example, includes letter patterns in addition to number sequences, so always consider both:

1. Is this following a simple alphabetical rule?
2. Or is it encoding a real-world ordered list?
   

Understanding these common patterns is the first step. When a new sequence question appears, mentally categorize it: Does it look arithmetic (constant addition/subtraction)? Geometric (multiplying/dividing)? Or something else like alternating or using a known series? Training yourself to quickly identify the pattern type will save precious time in the test.

Solving sequence problems under time pressure requires both logical strategy and smart time management. Here are some proven tips for tackling sequence questions efficiently:

Start with the Basics
First, look for simple patterns. Calculate the differences between consecutive numbers to check for a constant difference (arithmetic) or see if there’s a consistent multiplication factor (geometric). If the sequence isn’t obvious, examine the differences of differences: sometimes a second-level pattern (like differences increasing linearly) emerges.

Check for Alternating Patterns
If the sequence doesn’t make sense as a single progression, consider that two sequences might be interwoven. For example, look at the 1st, 3rd, 5th terms as one sub-sequence and the 2nd, 4th, 6th terms as another. This is a common trick in harder sequence questions.

Consider Common Series
Ask yourself if the numbers relate to known series (famous examples include Fibonacci numbers, prime numbers, powers of 2, factorials, etc.). Sometimes recognizing that, say, 120 appears (which is 5!, factorial of 5) or seeing 2, 3, 5, 7 (primes) could hint at the pattern.

Don’t Overcomplicate
The patterns in interviews are usually designed to be solved in under a minute, so they tend to be elegant rather than requiring brute force or extremely obscure math. Trust simple logic. For instance, if every other number ends in 8, there’s likely a straightforward reason. In that sense, trading sequence puzzles aren’t about deep mathematics: they’re about seeing an opportunity (pattern) quickly, often with child-like simplicity. Look for a clear rule that fits all given terms.

Use Logical Elimination (for Multiple Choice)
If the sequence question is multiple-choice, use the answer options to your advantage. Often you can rule out options that don’t fit a pattern. For example, if two possible next numbers continue an increasing trend but one option is much too large or too small, you can eliminate outliers. Elimination can save time especially if you partially identify the pattern.

Manage Your Time
In sequence tests, time is limited, but not as brutally as mental math speed tests. You might have on the order of 1 minute per question (e.g. 25 minutes for 26 questions in one firm’s test, or roughly 25 minutes for 24 questions in another). Still, you must allocate your time wisely. Don’t get stuck too long on one puzzling sequence: it’s often better to skip and return if time permits. Many tests allow you to skip or pass on a question without penalty unless you guess incorrectly. If wrong answers carry a penalty (as in some trading firm assessments), be strategic: it’s better to skip a question you’re truly unsure about than to guess randomly and lose points.

Stay Calm and Think Clearly
Pattern recognition can be hampered if you panic. If you feel stumped, take a quick breath and systematically review the sequence. Try writing down (if allowed) interim patterns like differences or ratios in your head. Sometimes the pattern “jumps out” on a second look. Maintaining composure will help your logical thinking.

Practice Under Test Conditions
Finally, simulate the test environment when practicing (more on this below). Get used to solving sequences with a timer ticking. This will train you to apply all the above strategies under realistic conditions, building your speed and confidence.

By applying these strategies, you’ll handle sequence problems more methodically. The key is pattern recognition, which is a skill that improves significantly with practice. Every sequence you solve (or even the ones you struggle with) trains your brain to spot another pattern faster the next time.

Like any skill, excelling at sequence puzzles comes down to consistent practice and gradually increasing challenge. Here’s how to prepare for sequence tests, especially using the tools available on Tradermath:

Use the Tradermath Sequence Trainer
Our customizable Sequence Trainer is designed to mirror real trading firm sequence tests. It lets you tailor your practice sessions to your needs. You can choose the difficulty level (Easy, Medium, Hard, or a mix), select the types of sequences (number sequences and/or letter sequences), set a time limit (from quick 1-minute drills up to longer 15-minute sessions), and pick the number of questions you want to attempt. You can even choose between open-ended questions (where you must fill in the answer with no options given) or multiple-choice format, with configurable number of answer options.

Open-Ended vs. Multiple-Choice Practice
Each format trains you in different ways. Open-ended questions are tougher because you have to fully work out the pattern and the answer on your own. This builds strong pattern recognition skills and mirrors the hardest scenario (some real tests are essentially open response). Multiple-choice questions are great for warming up and improving speed; they train you to quickly eliminate incorrect options and make educated guesses when needed. We recommend starting with multiple-choice if you’re a beginner to sequences, as it provides some cues, then progressing to open questions to solidify your skills once you’re more confident.

Practice Consistently in Short Sessions
It’s more effective to practice a little every day than to do a massive session once in a while. Aim for training 3-4 times a week for 5-15 minutes per session to keep your pattern-spotting skills sharp. Daily practice is even better. The idea is to make recognizing sequences almost second nature through repetition. Short, focused sessions help you retain these skills better than occasional long drills, your brain benefits from steady exposure and rest in between.

Start Simple and Ramp Up
If you’re new to sequence problems, begin with the basics. In the Tradermath Sequence Trainer, you might start with only arithmetic sequences selected, at an Easy difficulty, to nail down the fundamentals. Once you’re scoring well there, add other sequence types or increase the difficulty to Medium and Hard levels. For instance, geometric and Fibonacci sequences can be introduced for more advanced challenges once you’ve mastered arithmetic patterns. Similarly, you can try including letter sequences once you’re comfortable with numbers, as letters often add another layer of logic.

Track Your Progress
Take advantage of the performance analytics in the training platform. Tradermath’s tools track metrics like your accuracy, number of attempts, and improvement over time (accuracy trend and speed trend). Use these to identify where you struggle. Do certain pattern types consistently trip you up? Are you slower on, say, Fibonacci sequences? Target those weak spots in your practice. Tracking also keeps you motivated as you see your scores improve.

Increase Difficulty Strategically
As you progress, keep raising the bar. Reduce the time limit gradually to train solving under pressure, or increase the number of questions to build endurance. Mix multiple sequence types in one practice session to simulate real tests where you won’t know what pattern is coming next. A good rule of thumb is to aim for about 90% accuracy at a given level before making it harder. For example, if you can consistently get 90% of Easy questions right in practice, move on to Medium. This ensures you build confidence and accuracy first, then speed and difficulty.

Simulate Real Test Conditions
Before your actual interview assessments, do some full-length mock tests. Set the timer for the exact duration of the real test (if you know it, e.g. 15 minutes for a segment, or a full 20-25 minute test) and attempt a mix of questions without interruption. Tradermath offers realistic test modes that mimic the look and scoring of specific firms’ sequence tests (for example, a practice mode for the Flow Traders Sequences Test or the Akuna Capital Sequence Test). These give you a feel for the pacing and pressure of the genuine article. After each test, review your answers, understanding any mistakes is crucial to avoid repeating them.

Learn from Hard Problems
When you encounter a particularly challenging sequence that you can’t solve in time, don’t just shrug it off. Take it as a learning opportunity. Look up the explanation or discuss with others to figure out the pattern. This expands your “library” of patterns in mind. The next time you see something similar, you’ll solve it much faster. Some sequence puzzles can be quite clever, so the more patterns you’ve been exposed to, the better.

By following these preparation tips, you’ll build both the skill and the confidence to ace sequence tests. Remember that speed comes with familiarity! The first time you see a new pattern it might feel impossible, but after enough practice, you’ll recognize it at a glance. That moment when a sequence “clicks” instantly is what you’re working towards.

Mastering sequence problems is a journey, but it’s one well worth the effort for aspiring traders. Strong performance on sequence tests will set you apart in the recruitment process, showcasing your quick thinking and analytical prowess. More importantly, the pattern recognition abilities you develop will serve you in many aspects of a trading career, from spotting market patterns to devising strategies on the fly.

Focus on pattern recognition, practice regularly, and use the tools at your disposal. With a solid training regimen (for example, leveraging the Tradermath Sequence Trainer and other resources) and the strategies outlined above, you can significantly improve your sequence-solving skills. Many before you have gone from being stumped by sequence puzzles to breezing through them with practice and patience.

In quant trading interviews, every edge counts. By dedicating time to sequence training, you’ll not only be well prepared for the test itself but also sharpen a cognitive skill that’s key to success in fast-paced trading environments. Good luck, and happy pattern solving!