Number Sequence Practice
Number-series pattern recognition. Today's free drill comes from a fixed 180-day pool. No signup. Runs in your browser.
15 questions · 3 minutes · today's set
Arithmetic, geometric, quadratic, Fibonacci-like and alternating-step sequences. +1 per correct answer, −1 per wrong answer, skips are free. Everyone gets the same 15 questions today.
Five sequence patterns
Each question shows a few terms and asks for the next one. Questions come from five pattern families, each with its own tell:
| Arithmetic | Constant difference between terms: 4, 7, 10, 13, → next is 16 (+3 each step). |
|---|---|
| Geometric | Constant ratio between terms: 3, 6, 12, 24, → next is 48 (×2 each step). |
| Quadratic-feel | The gaps between terms grow by a constant amount: 1, 2, 4, 7, → next is 11 (the gaps themselves are 1, 2, 3, 4). |
| Fibonacci-like | Each term is the sum of the previous two: 2, 3, 5, 8, → next is 13. |
| Alternating-step | Two step sizes alternate: 5, 8, 6, 9, → next is 7 (+3, −2, +3, −2, …). |
How to check a proposed rule
The examples above each suggest a simple rule. Test that rule against every displayed transition before extending it. A short sequence does not determine a unique mathematical continuation: these answers follow the stated pattern, not the only rule that could fit the numbers.
Constant differences: 4, 7, 10, 13
Answer under the +3 rule: 16. Subtract each term from the next: 7 − 4 = 3, 10 − 7 = 3 and 13 − 10 = 3. Keep the same difference: 13 + 3 = 16. A common mistake is noticing only the first +3 and failing to check the remaining gaps.
Constant ratios: 3, 6, 12, 24
Answer under the ×2 rule: 48. Divide each term by its predecessor: 6/3 = 2, 12/6 = 2 and 24/12 = 2. Continue with 24 × 2 = 48. The differences grow, so adding the most recent gap of 12 would give 36 and break this rule.
Second differences: 1, 2, 4, 7
Answer under the increasing-gap rule: 11. First differences are 1, 2 and 3. Their differences are both 1, so the next first difference is 4. Add that to the last term: 7 + 4 = 11. The common error is adding the second difference directly to 7 instead of using it to update the gap.
Previous-two-term sum: 2, 3, 5, 8
Answer under the sum rule: 13. Check 2 + 3 = 5 and 3 + 5 = 8. The next term is therefore 5 + 8 = 13. Use the last two terms, not a fixed increment or a memorized Fibonacci sequence starting from 1.
Alternating steps and subsequences: 5, 8, 6, 9
Answer under the +3, −2 rule: 7. The gaps are +3, −2, +3, so the next gap is −2 and 9 − 2 = 7. As a cross-check, odd-position terms are 5, 6, then 7; even-position terms are 8, 9, then 10. Keep positions separate: taking the next even-position value would answer the wrong slot.
Next: try the timed 15-question sequence drill. It mixes these five families, so state the rule to yourself before entering the next number. If the rule is clear but the arithmetic is slow, use the mental math worked examples.
Practicing patterns alongside other reasoning skills
Sequence practice trains you to propose and check a rule from a few observations. Our CTC-style mixed simulation combines numerical, spatial, verbal and logic practice, so it also requires switching between methods. These are TradeMind training formats; use your invitation to check which skills and rules apply to a particular recruitment assessment.
Probability & EV practice
Probability has its own daily drill: Probability & EV Practice. For both skills in one test, take the 60-question Sequences & Probability test.
Related practice
- Realistic OA Trial: CTC-style, numerical/spatial/verbal/logic mixed
- Mental Math Practice: arithmetic speed drills and firm-specific formats
- How to prepare for a quant trading interview: the full pipeline and a study plan
Questions
What kinds of sequences are in the daily drill?
15 questions in 3 minutes, mixing arithmetic (constant difference), geometric (constant ratio), quadratic-feel (constant second difference), Fibonacci-like (each term is the sum of the previous two), and alternating-step patterns. Each question has an intended rule used to create its answer; a finite list of numbers can fit other rules too.
What's a good score on this drill?
11 of 15 is a reasonable target. This is a daily practice drill, so there is no firm cutoff or official pass mark. Use first attempts on different daily sets to judge progress, then try the longer Sequences & Probability practice test.
How do I get faster at spotting the pattern?
Always compute the differences between consecutive terms before guessing a named sequence. Arithmetic and geometric patterns show up in that first row of differences (or ratios). Quadratic-feel patterns show up one row down, in the differences of the differences. Only try Fibonacci-like or alternating-step once constant difference and constant ratio are ruled out. Checking in that order is faster than pattern-matching from memory.
Why is this separate from probability & EV now?
They are different skills: pattern recognition in a series, and probability and expected-value calculation. An older test combined them only because both are generic firm-test formats. This page covers sequences only. Probability has its own Daily Probability & EV drill.
Is there a longer, combined version?
Yes. The original 60-question Sequences & Probability test mixes both skills in one full-length fixed set. This daily drill is shorter, covers sequences only and rotates every day.