How do I know if my sequence is arithmetic or geometric?

In an arithmetic sequence, consecutive terms differ by a constant amount (add the common difference). In a geometric sequence, consecutive terms differ by a constant ratio (multiply by the common ratio). Select the matching type and enter that constant.

How is the sum of the first n terms calculated?

For arithmetic sequences, the sum uses Sₙ = n/2 × (2a₁ + (n−1)d). For geometric sequences (ratio ≠ 1), it uses Sₙ = a₁ × (1 − rⁿ) ÷ (1 − r).

Number Sequence Calculator

Find the nth term and sum of an arithmetic or geometric sequence.

How this is calculated

Arithmetic: aₙ = a₁ + (n−1)d. Geometric: aₙ = a₁ × r^(n−1)

Assumptions used in this calculation

Sequence type: The same "common difference / ratio" input is interpreted as an additive difference for arithmetic sequences or a multiplicative ratio for geometric sequences, based on the selected mode.

About this calculator

Calculates the nth term and the sum of the first n terms for arithmetic (add a common difference) or geometric (multiply by a common ratio) sequences.

Worked example

a₁=2, d=3, n=5 (arithmetic)

Result: 5th term = 14, sum of first 5 terms = 40

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Frequently asked questions

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Calculate powers (exponents) and nth roots.

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About this calculator

Frequently asked questions

How do I know if my sequence is arithmetic or geometric?

How is the sum of the first n terms calculated?

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