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The goal of this lesson is for students to encounter several situations in which it makes sense to find the sum of a sequence, defined here as adding up the value of the terms of the sequence. At this point, the number of terms students need to add is kept small since the summing is by hand. In a future unit students use polynomial identities to develop a formula to sum the first terms of any geometric sequence, so the emphasis here is on understanding what is being summed and why adding together terms in a sequence can make sense in some contexts.
The main activities in this lesson are meant to be relatively unscaffolded (MP1). This gives students the opportunity to make sense of the problems using the tools they have worked with throughout this unit, such as tables, graphs, and equations.