1. Infinite Geometric Series Recursion & Special Sequences 33 22 11 Definitions & Equations Writing & Solving Geometric Series Practice Problems

2. Definitions 2  Infinite Geometric Series  A geometric series that has no final value  Recursive Formula  Each term is formulated from one or more of the previous terms  Fibonacci Sequence  Each term is formulated by adding the two previous terms  1, 1, 2, 3, 5, 8, 13, 21, 34…  a n = a n-2 + a n-1

3. Sum of an Infinite Geometric Series  The sum (S) of an infinite geometric series with -1 < r < 1 is given by  If |r|≥1, the sum does not exist 3

4. Finding the Sum of an Infinite Geometric Series  Find the sum if it exits 4

5. Finding the Sum of an Infinite Geometric Series  Find the sum if it exits 5

6. Use a Recursive Formula Find the first five terms of a sequence in which a 1 =4 and a n+1 =3a n -2, n≥1. 6

7. Fibonacci Sequences in Nature 7

8. More Fibonacci Sequences in Nature 8

9. My Personal Favorite Fibonacci Sequence in Nature 9