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9-4 Arithmetic Series Today’s Objective: I can find the sum of an arithmetic series.

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The first four rows of chairs are set up for a meeting. The seating pattern is to continue through 20 rows. How many chairs will there be in all 20 rows? Series: Sum of the terms of a sequence Finite Series: Has first and last term 6 + 9 + 12 + 15 + 18 Infinite Series: Continues without end 3 + 7 + 11 + 15 +… 4 + 5 + 6 + 7 +… + 23 = 270 2 + 4 + 6 + ··· + 100 = 270

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7 + 11 + 15 + ··· + 207 – 5 + 2 + 9 + 16 +··· + 268 Arithmetic Series Explicit Formula = Linear Slope = Common Difference

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Find the sum of a Finite Arithmetic Series

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A company pays a $10,000 bonus to salespeople at the end of their first 50 weeks if they make 10 sales in their first week, and then improve their sales numbers by two each week thereafter. One salesperson qualified for the bonus with the minimum possible number of sales. How many sales did the salesperson make in week 50? p. 591: 9-45 mult. of 3 and 47 How many sales did the salesperson make in all 50 weeks?

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Calculator Notes: [2 ND ] [STAT] [►] [►] [5] [2 ND ] [STAT] [►] [5] explicit formula, x, lower limit, upper limit [ENTER]

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