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

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

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

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

Sequence using Factorials

Summation Notation

Summation Notation Examples

General Term of an Arithmetic Sequence

Example

Sum of the First n Terms of an Arithmetic Sequence

Examples

General Term of a Geometric Sequence

Examples

Sum of the First n Terms of a Geometric Sequence

Sum of an Infinite Geometric Seires

You try one: