Number Sequence Calculator
Identify whether a sequence of numbers is arithmetic or geometric, find its common difference or ratio, and predict the next terms.
Calculator Inputs
| Term | Remove row |
|---|---|
Add at least 3 terms, in order.
- Pattern Type
- arithmetic
- Common Difference / Ratio
- 3.00
- Next Term
- 14.00
- Next 3 Terms
- 14, 17, 20
About these results
CalcSpectrum calculators produce automated estimates using established formulas and the specific values you enter. Because real-world outcomes depend on input accuracy, mathematical assumptions, and rounding conventions, please verify critical figures with an appropriately qualified financial, tax, medical, legal, or other professional, as relevant.
How It's Calculated
Formula
This calculator recognizes two of the simplest and most common sequence patterns: arithmetic sequences, where each term is found by adding a constant common difference to the previous term (like 2, 5, 8, 11 — always add 3), and geometric sequences, where each term is found by multiplying the previous term by a constant common ratio (like 3, 6, 12, 24 — always multiply by 2). It checks for an arithmetic pattern first, then a geometric one; a constant sequence like 5, 5, 5 is reported as arithmetic with a common difference of 0. This tool deliberately only recognizes exact simple patterns — it is not a general pattern-guessing or AI inference engine, so sequences that don't fit a constant-difference or constant-ratio rule (or that would require dividing by a zero term to test a ratio) are reported as an unsupported pattern rather than a best-effort guess.
Worked Examples
Arithmetic sequence: 2, 5, 8, 11
- 5 − 2 = 3, 8 − 5 = 3, 11 − 8 = 3
- Common difference is constant: 3
- Next term: 11 + 3 = 14
Geometric sequence: 3, 6, 12, 24
- 6 ÷ 3 = 2, 12 ÷ 6 = 2, 24 ÷ 12 = 2
- Common ratio is constant: 2
- Next term: 24 × 2 = 48
Frequently Asked Questions
What's the difference between an arithmetic and a geometric sequence?
An arithmetic sequence has a constant amount added between consecutive terms (the common difference). A geometric sequence has a constant multiplier between consecutive terms (the common ratio). 2, 5, 8, 11 is arithmetic (always +3); 3, 6, 12, 24 is geometric (always ×2).
How is a constant sequence like 5, 5, 5 classified?
As arithmetic, with a common difference of 0. Arithmetic detection runs before geometric detection, so a constant sequence is never left ambiguous between the two.
Can this calculator recognize any pattern, like Fibonacci or squares?
No. This tool only recognizes simple arithmetic (constant difference) and geometric (constant ratio) patterns. It does not attempt to infer more complex or arbitrary patterns — a sequence like 1, 1, 2, 3, 5, 8 (Fibonacci) or 1, 4, 9, 16 (squares) is reported as an unsupported pattern.
Why does a sequence with a zero sometimes show as unsupported?
A geometric ratio is calculated by dividing consecutive terms, and dividing by zero is undefined. If a sequence contains a zero term and isn't already arithmetic, this calculator never attempts that invalid division — it reports the sequence as unsupported instead of guessing.
How many terms do I need to enter?
At least 3. Two terms are never enough to confirm a pattern is arithmetic or geometric rather than coincidence, so this calculator requires a minimum of 3 terms before it will detect a pattern.