This number sequence calculator finds the pattern in a list of numbers. Enter three or more terms and it identifies arithmetic, geometric, quadratic and Fibonacci-type sequences, gives the nth term formula, the next five terms, any term you choose and the sum of the first n terms.
Types of sequence
| Type | Example | nth term | Sum of first n terms |
|---|---|---|---|
| Arithmetic | 3, 7, 11, 15 | a + (n − 1)d | n/2 × (2a + (n − 1)d) |
| Geometric | 2, 6, 18, 54 | a × rn−1 | a(1 − rⁿ) ÷ (1 − r) |
| Quadratic | 2, 5, 10, 17 | an² + bn + c | Found from the formula |
| Fibonacci-type | 1, 1, 2, 3, 5 | aₙ₋₁ + aₙ₋₂ | Added term by term |
How to spot the pattern
- Subtract each term from the next. If the differences are equal, the sequence is arithmetic.
- Divide each term by the one before. If the ratios are equal, it is geometric.
- If the differences themselves change by a constant amount (equal second differences), it is quadratic.
- If each term is the sum of the two before it, it is Fibonacci-type.
Worked example
For 3, 7, 11, 15 the difference is always 4, so the nth term is 3 + 4(n − 1) = 4n − 1. The 20th term is 79, and the first 20 terms add up to 820.
Frequently asked questions
How many terms do I need to enter?
At least 3. Quadratic sequences need at least 4 so the pattern can be confirmed.
What if my sequence has no pattern listed here?
Many puzzles use other rules, such as squares plus a constant (which are quadratic) or alternating patterns. Try entering more terms.
What is the difference between a sequence and a series?
A sequence is a list of numbers; a series is the sum of the terms of a sequence.
Can a geometric sequence have a negative ratio?
Yes. With a ratio of −2, the sequence 1, −2, 4, −8 alternates between positive and negative.
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Last reviewed: October 2026. For information only; results are estimates; check important figures with a professional.