Sequence & Series
MathematicsAnalyze arithmetic and geometric sequences. Find the n-th term, common difference or ratio, recursive formula, and sum of finite or infinite convergent series.
Sₙ = 255
About this calculator
Sequences and series model periodic investment contributions, depreciation schedules, acoustic wave harmonics, and algorithmic runtime bounds in computer science.
This calculator identifies whether a progression is arithmetic (constant additive difference d) or geometric (constant multiplicative ratio r), solves for any n-th term aₙ, and computes the cumulative partial sum Sₙ.
How It Works & Formula
Arithmetic n-th term: aₙ = a₁ + (n-1)d, Sum: Sₙ = n/2(2a₁ + (n-1)d). Geometric n-th term: aₙ = a₁ · rⁿ⁻¹, Sum: Sₙ = a₁(1 - rⁿ)/(1 - r) for r ≠ 1, and S_∞ = a₁/(1 - r) for |r| < 1.
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