sekvenser

Sekvenser, or sequences, are ordered lists of elements indexed by natural numbers. Each term is written a_n, where n = 1, 2, 3, ... The terms can be numbers, objects, or symbols, and a sequence may be finite or infinite. In mathematics, sequences describe how a quantity evolves step by step.

Common numerical sequences include arithmetic sequences with constant difference d (a_n = a_1 + (n−1)d) and geometric sequences with constant ratio r (a_n = a_1 r^{n−1}). The Fibonacci sequence is defined by a_n = a_{n−1} + a_{n−2} with a_1 = a_2 = 1.

Convergence is central: a sequence (a_n) converges to a limit L if a_n approaches L as n grows. If no such L exists, the sequence diverges. Subsequence, monotonicity, and boundedness are used to study limits and continuity.

In computer science, sekvenser describe ordered data or token streams. In biology, DNA and protein sequences specify nucleotide or amino acid order. In linguistics and music, sequences capture patterns and repetitions, often analyzed statistically or algorithmically.

Historically, sequences underpin the idea of limits and series, and they remain foundational in analysis, probability, and numerical methods.