Sequence and Series Calculator - Arithmetic & Geometric

A sequence where each term after the first is obtained by adding a constant difference.

aₙ = a₁ + (n-1)d

Sₙ = n/2 × (2a₁ + (n-1)d)

Sₙ = n/2 × (a₁ + aₙ)

Where: a₁ = first term, d = common difference, n = number of terms

A sequence where each term after the first is obtained by multiplying by a constant ratio.

aₙ = a₁ × r^(n-1)

Sₙ = a₁ × (1 - r^n) / (1 - r) [r ≠ 1]

Sₙ = n × a₁ [r = 1]

Where: a₁ = first term, r = common ratio, n = number of terms

Sequence: An ordered list of numbers (terms)

Series: The sum of the terms in a sequence

Examples:

Arithmetic Sequence: 2, 5, 8, 11, 14, ...

Arithmetic Series: 2 + 5 + 8 + 11 + 14 + ...

🔢 Sequence and Series Calculator