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Activity 11.1 Arithmetic Series Overview: This activity is a worksheet that explores the number of seats in a theater, which can be modeled by an arithmetic series. The worksheet leads students through the process of finding the formula of the series by asking a series of directed questions. Students are then asked to identify which of four given series are arithmetic. Estimated Time Required: The activity should take approximately 20 minutes. Technology: None Concepts: Arithmetic series and the associated notation Discussion: When you generalize the structure of an arithmetic sequence, use caution in introducing the standard notation that uses subscripts. Activity 11.1 Arithmetic Series 1. Suppose a theater has 40 rows of seats; the first row contains 18 seats, and the number of seats increases by 2 per row. How many seats are in the theater? To answer this question (without adding up every single term), work through the following steps: a.) Write a sequence for the number of seats in consecutive rows, starting with 18 (the first row) b.) Now, write out the sum you are trying to find (use … in the middle to save space). c.) By pairing the first and last term, the second and next-to-last term, and so on, do you notice a pattern? How many seats are in the theater? d.) Now, find a formula for determining the number of seats in the nth row. e.) Can you relate the sum you found in part (c) to your formula in part (d) to find a general formula for the sum of the first n terms of this type of sequence? 2. Which of the following sequences are arithmetic? a.) an 1 n d.) 0.2, 0.02, 0.002, b.) 3 1 1 , , , 4 4 4 c.) an 3 3n