1. 11/5/20158-3 8-3 Arithmetic Series

2. 11/5/20158-3Series 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

3. 11/5/20158-3 Sigma Notation Means: The sum of terms 1 through 6 of the sequence defined by (4i + 1)

4. 11/5/20158-3 Sigma Notation

5. 11/5/20158-3 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.

6. The Story of Gauss… Third grader: Teacher tells the class to find the sum of the first 100 integers…. 11/5/20158-3

7. 11/5/20158-3 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?

8. 11/5/20158-3 Arithmetic Series

9. Example continued… Now revisit that last example and solve: 11/5/20158-3