Trainers & Games
Sequence Trainer
What number comes next? Spot the pattern before the timer runs out, a classic trading-interview warm-up.
Sequence Trainer
Spotting the pattern in a number sequence is a classic opener in quant and trading interviews. The trick: look at the differences between terms, and the differences of those differences, and check the ratios. A constant difference means arithmetic; a constant ratio means geometric; a steadily growing gap points to squares or another quadratic rule.
Learn how it works
Five worked examples. Read a couple before you dive in, try to answer first, then reveal the solution.
Arithmetic, constant difference
What comes next? 3, 7, 11, 15, ?
Show solution
First habit: look at the gaps between terms.
- 7 − 3 = 4, 11 − 7 = 4, 15 − 11 = 4
The difference is a constant 4, so it's arithmetic. Add 4 to the last term:
- 15 + 4 = 19
Geometric, constant ratio
What comes next? 3, 6, 12, 24, ?
Show solution
The gaps here grow (3, 6, 12...), so instead check the ratios:
- 6 ÷ 3 = 2, 12 ÷ 6 = 2, 24 ÷ 12 = 2
Each term is ×2 the one before, geometric. Multiply the last term:
- 24 × 2 = 48
Rule of thumb: constant gap → add; constant ratio → multiply.
Perfect squares
What comes next? 1, 4, 9, 16, ?
Show solution
These are the counting numbers squared:
- 1 = 1², 4 = 2², 9 = 3², 16 = 4²
So the next is 5² = 25. Memorize the square pattern (1, 4, 9, 16, 25, 36, 49...), it shows up constantly and is easy to miss if you only stare at the differences.
Fibonacci-like, sum of the previous two
What comes next? 2, 3, 5, 8, 13, ?
Show solution
The differences aren't constant and there's no clean ratio, so try adding neighbours:
- 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13
Each term is the sum of the two before it. So:
- 8 + 13 = 21
Growing differences, the second layer
What comes next? 2, 6, 12, 20, ?
Show solution
The gaps aren't constant, so look at the differences of the differences:
- gaps: 6 − 2 = 4, 12 − 6 = 6, 20 − 12 = 8
- those gaps grow by a steady +2 each time (4, 6, 8...)
So the next gap is 8 + 2 = 10, giving 20 + 10 = 30. The layered trick, differences, then differences of those, cracks most "growing gap" sequences.
What you'll learn
Pattern recognition under time pressure, arithmetic, geometric, and recursive sequences of the kind trading interviews love to open with.