Sequence Calculator (Arithmetic & Geometric — nth Term & Sum)

Use this free sequence calculator for arithmetic and geometric sequences. Enter the first term, the common difference (arithmetic) or common ratio (geometric), and a term number n, and you’ll get the nth term, the sum of the first n terms, and a preview of the sequence — with each formula substituted step by step.

How to use the sequence calculator

1. Pick the type: arithmetic or geometric.
2. Enter the first term, the common difference or ratio, and the term number n.
3. Read the nth term, the sum, and the listed terms, with the steps.

The formulas

Arithmetic: the nth term is aₙ = a₁ + (n − 1)d and the sum is Sₙ = n/2 · (2a₁ + (n − 1)d). Geometric: the nth term is aₙ = a₁ · rⁿ⁻¹ and the sum is Sₙ = a₁(rⁿ − 1)/(r − 1).

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Frequently asked questions

What is the nth term of an arithmetic sequence?

aₙ = a₁ + (n − 1)d. With a₁ = 3 and d = 5, the 10th term is 3 + 9×5 = 48.

How do you find the sum of a geometric sequence?

Sₙ = a₁(rⁿ − 1)/(r − 1) for r ≠ 1. With a₁ = 2, r = 3, n = 5 the sum is 242.

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What’s the difference between arithmetic and geometric?

Arithmetic sequences add a fixed amount (the common difference); geometric sequences multiply by a fixed amount (the common ratio).

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