Sequence Calculator
Arithmetic and geometric sequences: the nth term, the sum and more.
Calculate
How to use this calculator
Choose the type of sequence, enter the first term, the common difference (or ratio) and the position n. You get the nth term, the sum of the first n terms, and the first few terms.
How it's calculated
Arithmetic: aₙ = a + (n − 1)d and Sₙ = n/2 × (2a + (n − 1)d). Geometric: aₙ = a × rⁿ⁻¹ and Sₙ = a(1 − rⁿ) ÷ (1 − r). If |r| < 1 the sum to infinity is a ÷ (1 − r).
Worked example
Arithmetic with a = 3, d = 4: a₁₀ = 3 + 9 × 4 = 39 and S₁₀ = 5 × (6 + 36) = 210.
Frequently asked questions
How do I tell the type?
If you add the same number each time it is arithmetic. If you multiply by the same number it is geometric.
Can the difference or ratio be negative or a fraction?
Yes, both are allowed.
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Last updated October 2026. Results are for learning and guidance; always check important work. Calculations run in your browser and are not stored.