11/5/20158-3 8-3 Arithmetic Series. 11/5/20158-3Series Series – The sum of terms of a sequence Infinite Series – The sum of all terms in a sequence Finite.

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Presentation transcript:

11/5/ Arithmetic Series

11/5/ Series Series – The sum of terms of a sequence Infinite Series – The sum of all terms in a sequence Finite Series – The sum of a set number of terms of a sequence

11/5/ Sigma Notation Means: The sum of terms 1 through 6 of the sequence defined by (4i + 1)

11/5/ Sigma Notation

11/5/ Arithmetic Series Arithmetic Sequence – A sequence where the difference between consecutive terms is constant (Finite) Arithmetic Series – The sum of the terms of an Arithmetic Sequence.

The Story of Gauss… Third grader: Teacher tells the class to find the sum of the first 100 integers…. 11/5/

11/5/ Arithmetic Series Example: A factory worker has to fill 100 boxes. He filled the first box in 13 minutes, but got faster by the same amount each time. The last box took him 8 minutes to fill. What was the total time if took to fill all 100 boxes? Example: A new business decides to rank its 9 employees and pay them amounts in an arithmetic sequence with a constant difference of $500/year. If the total amount paid to the employees is $250,000 a year, what will each of them make for a salary?

11/5/ Arithmetic Series

Example continued… Now revisit that last example and solve: 11/5/