Alg2.1 Sequences and Functions

This unit provides an opportunity to revisit representations of functions (including graphs, tables, and expressions) at the beginning of the Algebra 2 course, and also introduces the concept of sequences. Through many concrete examples, students learn to identify geometric and arithmetic sequences. Beginning with an invitation to describe sequences informally, students progress to writing terms of sequences arising from mathematical situations, using representations such as tables and graphs. They progress to using function notation to define sequences recursively and then explicitly for the \(n^{\text{th}}\) term. Throughout the unit, students learn that sequences are functions and that geometric and arithmetic sequences are examples of the exponential and linear functions they learned about in previous courses, defined on a subset of the integers. In the last part of the unit, students use sequences to model several situations represented in different ways. Finally, students encounter some situations where it makes sense to compute the sum of a finite sequence. A formula for such a sum is developed in a future unit.