1. Welcome to MM250! Unit 7 Seminar To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right to enlarge the pod. To maximize chat, minimize roster by clicking here

2. MM250 Unit 7 Seminar Agenda Sequences Arithmetic Sequences Geometric Sequences Series Mathematical Induction

3. Sequence Notations Each term is labeled a n For example The first term would be a 1 The second term would be a 2 The third term would be a 3

4. General Form for a Sequence a n =5n+2 Using this formula we have a 1 = 5(1)+2 = 7 a 2 = 5(2)+2 = 12 a 3 = 5(3)+2 = 17 a 4 = 5(4)+2 = 22 and so on

5. Recursion Formula a n = 5a n-1 +6 with a 1 =1 a 1 = 1 (given) a 2 = 5(1)+6 = 11 a 3 = 5(11)+6 = 61 a 4 = 5(61)+6 = 311 and so on

6. Sequence using Factorials

8. Summation Notation

9. Summation Notation Examples

10. General Term of an Arithmetic Sequence

11. Example

12. Sum of the First n Terms of an Arithmetic Sequence

13. Examples

14. General Term of a Geometric Sequence

15. Examples

16. Sum of the First n Terms of a Geometric Sequence

17. Sum of an Infinite Geometric Seires

18. You try one: