1. Warm UP! 1.Indentify the following as Arithmetic, Geometric, or neither: a.2, 5, 8, 11, … b.b. 2, 6, 24, … c.c. 5, 10, 20, 40, … 2. Demonstrate you know the difference in an arithmetic series and sequence by writing one of each. Both should have a first term of 2 and common difference of 3. 3. Find the 50 th term of the sequence a n = 2n – 6

2. Summation Notation AKA Sigma Notation i = Index of Summation (lower limit) n = upper limit

3. Partial Sum of an Arithmetic Series The sum of the terms from 1 to n of an arithmetic sequence can be found using this formula: n=number of terms

4. nth Partial Sum The sum of the first n terms of an infinite sequence is called the nth partial sum.

5. Example: Find the Sum Find the sum: 1+3+5+7+9+11+13+15+17+19

6. Example: Find the Sum Find the sum of the integers from 1 to 100.

7. Example: Find the Sum Find the sum: 81+77+73+…+5 860

8. Find the 78 th partial sum:

9. Evaluate the sum:

10. Example 6: Sigma Notation

11. Example: Find the Partial Sum Find the 150 th partial sum of the AS. – 5,16,27,38,49,…

12. Example: An A.S. has a 1 = 19 and a 2 = 32 1.Find the common difference 2.Find a 300 3.Find S 300 4.Find n if a n = 7377 5.Find n if S n = 1086 13 3,906 588,750 567 12

13. Example: Applications An auditorium has 20 rows of seats. There are 20 seats in the 1 st row, 21 seats in the second row, 22 seats in the 3 rd row, and so on. How many seats are there in all 20 rows?

14. Example: Applications A small business sells $10,000 worth of products during its first year. The owner of the business has set a goal of increasing annual sales by $7500 each year for 19 years. Assuming that this goal is met, find the total sales during the first 20 years this business is in operation.

15. Example: Applications Shelbi starts an exercise program. At the first workout she does 5 push ups. The next workout she does 8 push ups. She decides to let the number of push ups in each workout be a term in a sequence. Find the number of pushups she does on the tenth workout. Also, find the total number of pushups she has done after 10 workouts. 32 185

16. sum of a finite geometric series

17. Ex. 6 Find the sum: = 5.714

18. Ex. 6 Find the sum: = 98,301

19. Find the sum of the first 60 terms of the sequence: a n = -3( 2 ) n-1 = -49,149

20. What are your questions?