PatternLab

Number Pattern Detector

Automatically finds arithmetic or geometric structure.

Sequence

Pattern

Arithmetic (common difference 3)

Predicted next term: 17

What you entered

Terms: 5

1
Check consecutive differences
5−2, 8−5, 11−8, 14−11= 3, 3, 3, 3
2
All differences equal → arithmetic sequence
common difference = 3= arithmetic
3
Predict the next term
14 + 3= 17

Result

Pattern: Arithmetic (common difference 3)

This sequence follows a constant-difference (arithmetic) pattern — the next term should be 17.

Recognising arithmetic and geometric patterns

The calculator checks for a constant difference between terms, then for a constant ratio, and predicts the next value.

Sequence	Pattern found	Next term
2, 4, 6, 8	Arithmetic, common difference 2	10
5, 10, 15, 20	Arithmetic, common difference 5	25
1, 2, 4, 8	Geometric, common ratio 2	16
3, 6, 12, 24	Geometric, common ratio 2	48
1, 4, 9, 16	No arithmetic or geometric pattern	not predicted

The last row is the honest limitation and worth knowing: 1, 4, 9, 16 is the sequence of perfect squares, an obvious pattern to a human but neither arithmetic nor geometric, so the calculator correctly reports that it finds neither rather than guessing. Its differences are 3, 5, 7 - themselves arithmetic, which makes it a quadratic sequence. Rows three and four share a ratio of 2 from different starting points, since the ratio describes the growth rather than the values.

Two common structures to check first

Most simple number patterns are either arithmetic (constant difference between terms) or geometric (constant ratio between terms) — checking both is usually the fastest way to spot the rule behind a sequence.

Why pattern recognition matters

Spotting the underlying rule lets you predict future terms without listing every one — useful for everything from IQ-test-style sequence questions to noticing a real trend in data.

Frequently asked questions

My sequence is 3, 7, 11, 15 — what comes next?

The differences between consecutive terms are all 4 (7−3, 11−7, 15−11), so this is arithmetic with d = 4. Next term: 15 + 4 = 19. The pattern detector confirms this and predicts subsequent terms too.

How is this different from the arithmetic and geometric sequence calculators?

Those calculators require you to already know the type and parameters (first term, common difference or ratio). This pattern detector figures out the type automatically from the numbers you enter — useful when you're not sure whether a pattern is arithmetic, geometric, or something else.

What if my sequence isn't arithmetic or geometric?

Some sequences follow other rules — quadratic (differences of differences are constant), Fibonacci-like (each term is the sum of the two before it), or more complex patterns. This tool checks the two most common types; for more exotic patterns, try looking at second differences or ratios of consecutive terms manually.