Number Sequence Calculator

An arithmetic sequence is a list of numbers where each term increases by a fixed amount called the common difference (d). For example, 2, 5, 8, 11 has a common difference of 3. The nth term is a + (n−1)d, and the sum of the first n terms is n/2 × (2a + (n−1)d).

A geometric sequence multiplies each term by a fixed value called the common ratio (r). For example, 3, 6, 12, 24 has a common ratio of 2. The nth term is a × r^(n−1), and the sum of the first n terms is a × (1 − r^n) ÷ (1 − r) when r is not 1.

For an arithmetic sequence, use a + (n−1)d. For a geometric sequence, use a × r^(n−1). Enter the first term, the common difference or ratio, and the position n, and this calculator returns that term along with the running sum and a preview of the sequence.

A sequence is an ordered list of numbers (the terms). A series is the sum of those terms. This calculator gives you both: the individual nth term of the sequence and the series total — the sum of the first n terms.

Yes. A negative common difference makes an arithmetic sequence decrease (10, 7, 4, 1…). A common ratio between 0 and 1 makes a geometric sequence shrink toward zero (16, 8, 4, 2…), and a negative ratio makes the terms alternate sign. This calculator handles all of these cases.