General Term Formula
A formula for the n-th term from the first terms of a sequence, with a check and the next terms.
Separate numbers with spaces, semicolons or new lines; fractions as 1/6. Numbering starts from n = 1. The more terms you enter, the more reliable the result.
This calculator finds a formula for the n-th term from the first terms of a sequence and checks it on the numbers you entered.
What it recognises
- arithmetic and geometric sequences;
- polynomials, when the difference table reaches a constant level;
- the form A · qⁿ⁻¹ + C, factorials, fractions 1 / (an + b), alternating signs;
- Fibonacci-type recurrences.
Example. 2, 6, 12, 20, 30: the differences are 4, 6, 8, 10 and the second differences equal 2, so aₙ = n² + n.
An important limit
A few numbers do not determine a sequence uniquely, because a polynomial can pass through any points. If there is no simple pattern, the calculator says so plainly and shows such a polynomial as one possible option.
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