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9-4Arithmetic Series Today’s Objective: I can find the sum of an arithmetic series.
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? • 4 + 5 + 6 + 7 + . . . + 23 • = 270 2 + 4 + 6 + ··· + 100 • = 270 Sum of the terms of a sequence Series: Finite Series: Has first and last term 6 + 9 + 12 + 15 + 18 Infinite Series: Continues without end3 + 7 + 11 + 15 + . . . Sum of a Finite Arithmetic Series
Summation Notation – 5 + 2 + 9 + 16 +··· + 268 7 + 11 + 15 + ··· + 207 Arithmetic Series Explicit Formula = Linear Slope = Common Difference
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? • How many sales did the salesperson make in all 50 weeks? p. 591: 9-45 mult. of 3 and 47