This chapter serves as a mathematical introduction to the concept of sequences, defining them as ordered lists where each number is a specific term identified by its position. It explores how to recognize and predict patterns through explicit rules, which calculate a term’s value directly from its position number $n$, and recursive rules, which determine a term based on its relationship to previous values. The material highlights classic examples like triangular and square numbers, alongside historical insights into the Virahānka-Fibonacci sequence and the summation formulas of Āryabhaṭa. Ultimately, the purpose of the chapter is to distinguish between two fundamental types of progressions: arithmetic progressions, characterized by a constant difference between terms, and geometric progressions, defined by a constant multiplier or common ratio.