Arithmetic
What comes next? 35, 26, 17, 8, -1, ?
Answer and worked solution
Answer: -10
Arithmetic: add -9 each time. Next term: -10. Speed tip: write the differences first; if they aren't constant, try ratios, then look at alternate terms.
Number sequences: interview questions and key results
Next-term puzzles, as in Optiver and Maven screens. The results to know for quant trading interviews, then a worked example of each of the 8 question types. Free, no sign-up.
Practise endless questions like these
Key results
- First try differences; if they change, take second differences.
- No pattern in differences? Try ratios (geometric, ×k ± c).
- Check alternate terms for two interleaved sequences.
- Recognise squares, cubes and Fibonacci instantly.
Worked examples (8)
Try each one before opening the solution. In the app, every type generates fresh numbers each time.
Geometric
What comes next? 6, -12, 24, -48, 96, ?
Answer and worked solution
Answer: -192
Geometric: multiply by -2. Next term: -192. Speed tip: write the differences first; if they aren't constant, try ratios, then look at alternate terms.
Squares ± c
What comes next? 15, 24, 35, 48, 63, ?
Answer and worked solution
Answer: 80
Squares minus 1: n² for n = 4, 5, … (differences grow by 2). Next term: 80. Speed tip: write the differences first; if they aren't constant, try ratios, then look at alternate terms.
Fibonacci-style
What comes next? 1, 4, 5, 9, 14, 23, ?
Answer and worked solution
Answer: 37
Fibonacci-style: each term is the sum of the previous two. Next term: 37. Speed tip: write the differences first; if they aren't constant, try ratios, then look at alternate terms.
Second differences
What comes next? 6, 7, 12, 21, 34, 51, ?
Answer and worked solution
Answer: 72
The differences go up by 4 each time (1, 5, 9, …). Next term: 72. Speed tip: write the differences first; if they aren't constant, try ratios, then look at alternate terms.
Interleaved sequences
What comes next? 5, 22, 10, 20, 15, 18, ?
Answer and worked solution
Answer: 20
Two interleaved sequences: odd positions add 5, even positions subtract 2. Next term: 20. Speed tip: write the differences first; if they aren't constant, try ratios, then look at alternate terms.
Multiply-and-add
What comes next? 5, 16, 49, 148, 445, ?
Answer and worked solution
Answer: 1336
Each term is 3× the previous plus 1. Next term: 1336. Speed tip: write the differences first; if they aren't constant, try ratios, then look at alternate terms.
Cubes
What comes next? 1, 8, 27, 64, 125, ?
Answer and worked solution
Answer: 216
Cubes: n³ for n = 1, 2, …. Next term: 216. Speed tip: write the differences first; if they aren't constant, try ratios, then look at alternate terms.
Other topics
Dice & coins · Cards & combinatorics · Conditional & Bayes · Expected value & games · Random walks & martingales · Markov chains & order statistics · Options · Classic brainteasers · Distributions · Variance & covariance · Estimation & testing · Regression & correlation · Returns, risk & sizing · Time series
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