A sequence is an ordered list of numbers. Each number is a term. The order matters: 1, 2, 3 is different from 3, 2, 1. Sequences can be finite or infinite. They follow rules, though the rule may not be obvious.

Arithmetic sequences add a constant each step. Geometric sequences multiply by a constant. The Fibonacci sequence adds the two previous terms. Sequences can also be defined recursively or by a formula for the nth term.

Sequences appear in mathematics, computer science, and nature. They model population growth, financial payments, and iterative algorithms. The study of sequences leads to series, limits, and convergence. Understanding them is essential for calculus and analysis.

• Ordered list of numbers
• Terms follow a pattern or rule
• Can be finite or infinite
• Foundation for series and limits