Find any term and sum of arithmetic or geometric sequences instantly
Sequence Type
Each term increases (or decreases) by a fixed common difference: aₙ = a₁ + (n−1)d
Parameters
Results
First 8 terms of the sequence
Formula Reference
Arithmetic Sequence
aₙ = a₁ + (n−1)d
nth term
Sₙ = n/2 · (2a₁ + (n−1)d)
Sum of first n terms
Geometric Sequence
aₙ = a₁ · r^(n−1)
nth term
Sₙ = a₁ · (1−rⁿ) / (1−r)
Sum of first n terms (r ≠ 1)
Use this free number sequence calculator to find the nth term and sum of any arithmetic or geometric sequence. Enter your first term and common difference (arithmetic) or common ratio (geometric), set n, and get an instant answer — including a visual preview of the first terms. Ideal for students, teachers, and anyone working through algebra or precalculus problems.
The nth term of an arithmetic sequence is aₙ = a₁ + (n−1)d, where a₁ is the first term, d is the common difference, and n is the position of the term.
The sum of the first n terms of a geometric sequence is Sₙ = a₁ · (1 − rⁿ) / (1 − r) when r ≠ 1, or Sₙ = n · a₁ when r = 1.
In an arithmetic sequence, consecutive terms differ by a fixed amount called the common difference (e.g. 3, 7, 11, 15). In a geometric sequence, each term is multiplied by a fixed common ratio (e.g. 2, 6, 18, 54).
Yes. A negative common ratio causes the terms to alternate in sign. For example, with a₁ = 1 and r = −2, the sequence is 1, −2, 4, −8, 16, …