A sequence is an ordered list of numbers following a specific pattern or rule.
Sequences can be finite or infinite. Arithmetic sequences have a constant difference between consecutive terms (d). Geometric sequences have a constant ratio (r). Other sequences include Fibonacci, quadratic, and recursive sequences. The nth term formula gives a direct expression for any term. Sequences are used in computer science (algorithms), finance (interest), and modeling natural phenomena.
Sequences have been studied since ancient times. Archimedes used sequences to approximate ฯ. The Fibonacci sequence was introduced in 1202. The concept of convergence of sequences was formalized by Cauchy and Weierstrass in the 19th century, forming the foundation of analysis.