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F5 Sequences
This unit both introduces the concept of sequences, and also provides an opportunity to revisit various representations of functions (including graphs, tables, and expressions) at the beginning of the Algebra 2 course. Through many concrete examples, students learn that geometric sequences are characterized by a common ratio, and arithmetic sequences are characterized by a common diVerence.
After several lessons describing such sequences informally, students learn to describe them more formally using recursive and closed-form deSnitions. In previous courses, students wrote expressions deSning linear and exponential functions. In this unit, students encounter tables and graphs that relate the number giving the position of the term and value of the term for arithmetic and geometric sequences. These representations
are familiar from students' earlier study of linear and exponential functions, so they can build on prior knowledge to write closed-form deSnitions of arithmetic and geometric sequences. The closed-form deSnitions are also built up through expressing regularity in repeated reasoning (MP8). For example, the geometric sequence 6, 18, 54, 162, . . . could be written which makes it easy to see that the th term can be deSned (assuming we start at the 0th term, or )
In order to emphasize that sequences are functions, function notation is used to deSne sequences. For example the arithmetic sequence 2, 6, 10, 14, . . . might be deSned
for or
In the last part of the unit, students model several situations with sequences represented in diVerents ways (MP4). This isn't meant to be full-blown modeling, but to touch on some practices that must be attended to while modeling, such as choosing a good model and expressing numbers with an appropriate level of precision. Students also recognize that a sequence is a function whose domain is a subset of the integers. Finally, students encounter some situations where it makes sense to compute the sum of a Snite sequence. Developing a formula for such a sum occurs in a future unit.
A3 Polynomials
In previous courses, students learned about linear and quadratic functions. They rewrote expressions for these functions in diVerent forms to reveal structure and identiSed key features of their graphs, such as intercepts. In this unit, students will expand their earlier
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Course Guide Algebra