ABSTRACT
This chapter aims to characterize sequences as recursive relations while introducing the first-order recursive sequences. It recalls various sorts of sequences such as linear sequence; summation-type sequence; geometric sequence; and factorial-type sequence. The chapter then directs us to deeper understanding of the new categories of sequences and their unique traits. The study of a linear sequence is expressed as a recursive formula and as an Initial Value Problem. The chapter transitions to solving recursive sequences explicitly by inductively obtaining a formula and solving an Initial Value Problem. It examines the varieties of first-order recursive sequences such as: linear homogeneous; linear nonhomogeneous; and linear nonautonomous. The chapter inductively determines an explicit solution to specific nonautonomous recursive sequences.
