Introduction to Sequences

In this lesson, we will introduce the concept of a sequence. A sequence is a function that computes an ordered list of numbers. When studying sequences, we will come across both infinite and finite sequences. An infinite sequence is a function with the set of positive integers as its domain. A finite sequence is a function with a limited set of positive integers as its domain. The domain would start with 1 and then increase by increments of 1 up to some final value. For example, the sequence of natural-number multiples of 3: 3, 6, 9, 12, 15, 18,..., is infinite. The sequence of the number of pages read each day in a five-day reading challenge: 10, 15, 20, 25, 30, is finite. A sequence can be defined explicitly or recursively. With a recursive definition, each term after the first term or the first few terms is defined using an expression involving the previous term or terms. With an explicit definition, the formula will not depend on any previous term. Our exercises for this section will focus on finding the first few terms of a given sequence.