A mathematical sequence is a list of numbers arranged in a specific order, following a particular rule or pattern. Each number in the sequence is called a term, and the position of each term is usually indicated by its index. For example, in the sequence 2, 4, 6, 8, each term increases by 2. Sequences can be finite, having a limited number of terms, or infinite, continuing indefinitely. They can be arithmetic, where each term is generated by adding a constant value, or geometric, where each term is produced by multiplying by a constant. Understanding sequences is fundamental in various areas of mathematics.