Page 140 - IM_Algebra2_FL Print Sample.pdf

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Activity Synthesis
Display the two closed-form de nitions from this task for all to see:
Ask students which de nes a sequence that is geometric and arithmetic, and label them. Ask students which function could be described as exponential and linear, and label them. What makes a function exponential or linear? See what students can recall from their previous studies, and write these recollections for all to see. They might identify features of these equations, or mention growth or decay factors, constant rate of change, or initial conditions. They might mention the characteristic shape of a graph representing each type of function. At this point, we are just trying to draw out anything they remember, not insist that they know anything in particular.
In previous lessons, we have seen recursive de nitions of functions. Add the recursive de nitions to
the display: and Tell students that
the forms they created in this activity are known as closed form de nitions. They allow us to nd any term in a sequence without needed to nd all the terms that lead up to it. Demonstrate this by showing how each form would be used to nd and
7.3 Tenth Terms
10 minutes
In this activity, students practice identifying, and then writing, closed-form de nitions of arithmetic and geometric sequences. They also encounter sequences that start with either a term 0 or term 1 and consider how that a ects the expression representing a given term.
Making a spreadsheet available gives students an opportunity to choose appropriate tools strategically (MP5).
Unit 1 Lesson 7: Closed Form De nitions 75