🔢 Number Sequence Calculator
Find the nth term and sum of arithmetic and geometric sequences.
Arithmetic and Geometric Sequences
An arithmetic sequence has a constant difference between terms: aₙ = a₁ + (n-1)d. A geometric sequence has a constant ratio: aₙ = a₁ × rⁿ⁻¹. These sequences model linear growth (arithmetic) and exponential growth (geometric) in real-world scenarios.
Sum Formulas
Arithmetic sum: Sₙ = n/2 × (2a₁ + (n-1)d). Geometric sum: Sₙ = a₁(1 - rⁿ)/(1 - r) for r ≠ 1. These formulas are used in finance (annuities), physics (series circuits), and computer science (algorithm analysis).
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