11SEQUENCES
In math, we often work with patterns. In this chapter, we discuss a special type of numerical pattern called a sequence, which is a list of ordered numbers called terms. We also define a sequence as a function whose domain is the set of whole numbers or counting numbers.
11.1 Writing Recursive Formulas for Sequences
Let's start by looking at the following sequence: 3, 7, 11, 15, 19, 23, … What is the next number? How can we describe this sequence in words? We see that the numbers in the sequence follow a pattern. In this case, we add 4 to each term to get the next one: 3 + 4 = 7, 7 + 4 = 11, 11 + 4 = 15, and so on. However, describing this sequence as “add 4 to a term to get the next one” won't uniquely identify it. This defines ...
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