Pattern recognition is the foundation of mathematical thinking. Most IQ tests start with sequences — for good reason.
How to Play: Each question shows a number sequence. Pick the next number from 4 options. 10 random per round.
Result
Top 13 Number Sequence Patterns
Number sequences appear in mathematics, physics, biology, and finance. The four most common types are arithmetic (constant difference), geometric (constant ratio), Fibonacci (sum of previous two), and powers (n², n³, etc.). Recognizing the pattern in 5–10 seconds is a marker of high numerical reasoning.
| # | Sequence | Next Number |
|---|---|---|
| 1 | 2, 4, 6, 8, ? | 10 |
| 2 | 3, 6, 12, 24, ? | 48 |
| 3 | 1, 1, 2, 3, 5, ? | 8 |
| 4 | 1, 4, 9, 16, ? | 25 |
| 5 | 100, 90, 81, 73, ? | 66 |
| 6 | 2, 6, 18, 54, ? | 162 |
| 7 | 1, 3, 7, 15, 31, ? | 63 |
| 8 | 5, 10, 17, 26, ? | 37 |
| 9 | 2, 5, 10, 17, 26, ? | 37 |
| 10 | 1, 8, 27, 64, ? | 125 |
| 11 | 1, 2, 4, 7, 11, ? | 16 |
| 12 | 3, 3, 6, 9, 15, ? | 24 |
| 13 | 2, 3, 5, 7, 11, ? | 13 |
How to Spot a Number Sequence Pattern
The fastest sequence-detection technique is to compute differences between consecutive terms. If the difference is constant (e.g., 2, 5, 8, 11 → +3 each time), it’s arithmetic. If the differences themselves form an arithmetic sequence (1, 4, 9, 16 → differences 3, 5, 7, 9, which differ by +2), it’s a quadratic — usually n² or related.
Geometric sequences multiply by a constant ratio. 3, 6, 12, 24 doubles each time. 100, 50, 25, 12.5 halves each time. The pattern jumps out from looking at ratios rather than differences. If the second-to-last term divides the last term cleanly, you likely have a geometric sequence.
Fibonacci sequences (and their cousins) sum two prior terms to get the next: 1, 1, 2, 3, 5, 8, 13, 21. They appear in pinecones, sunflower seeds, rabbit population models, and (controversially) financial markets. The defining check: does each term equal the sum of the two before it?
More exotic patterns include alternating operations (×2, +1, ×2, +1…), nested sequences (each term is the previous term plus a growing add), and prime number lists (2, 3, 5, 7, 11, 13, 17, …). When standard tricks fail, check if the sequence might be primes, factorials (1, 2, 6, 24, 120), or powers of n.
Frequently Asked Questions
How do I quickly identify a sequence type?
Subtract consecutive terms first. If the differences are constant, it’s arithmetic. If the differences themselves grow constantly, it’s quadratic. If terms multiply by a constant factor, it’s geometric.
What is the Fibonacci sequence?
1, 1, 2, 3, 5, 8, 13, 21, 34… where each term is the sum of the previous two. Named after Leonardo of Pisa (Fibonacci) who introduced it to Europe in 1202 to model rabbit population growth.
Are number sequences part of IQ tests?
Yes. Most IQ tests (Wechsler, Stanford-Binet, Raven’s Progressive Matrices) include numerical and pattern-completion sequences. They measure ‘fluid intelligence’ — the ability to solve novel problems.
Why is 1, 4, 9, 16 important?
These are squares: 1², 2², 3², 4². The pattern is n² where n increments by 1. The differences (3, 5, 7) are also a clue — odd numbers in sequence indicate squaring.
What's the trick for 1, 1, 2, 3, 5, 8?
Fibonacci. Each term is the sum of the two before it. After 8 comes 13 (5+8), then 21 (8+13), and so on.
Note: Sequences are widely-used standard test patterns. Check arithmetic difference first, then geometric ratio, then Fibonacci, then squares/cubes.
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