Arithmetic and Geometric Series Calculator

Find any term and the sum of the first n terms of an arithmetic or geometric sequence.

What Do You Want to Find?
Fractions and decimals both work.
Sum of n terms
nth term
First terms
Infinite sum
Work

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Sequence and Series Formulas

Arithmetic: aₙ = a₁ + (n − 1)d   Sₙ = n(a₁ + aₙ) ÷ 2
Geometric: aₙ = a₁rⁿ⁻¹   Sₙ = a₁(1 − rⁿ) ÷ (1 − r)   S∞ = a₁ ÷ (1 − r) when |r| < 1

Worked Example

Tips

Compound interest is a geometric sequence; a savings plan that adds the same amount each month without interest is arithmetic.