1. Figure out how to work with infinite series when i=0 vs i=1 Slide 12

2. Geometric Sequences and Series Objectives: To recognize a pattern as a geometric sequence To formulate the sequence equation as a function of n To sum up a finite OR INFINITE geometric sequence

3. Is the following sequence arithmetic 10, 20, 40, 80, 160,… NO!! The difference from one term to the next is NOT a constant difference But, something is going on here. 102040

4. Vocabulary Geometric Sequence: A sequence where the ratio of consecutive terms are the same Again, work RIGHT TO LEFT r is a common ratio

5. #1 Determine if the sequence is geometric 1.5; 15; 45; 135 7.

6. Finding the equation for the nth term of a geometric sequence A geometric sequence of an equation is given by a n = a 1 r n-1 r is the common ratio Consider 2, 4, 8, 16, …

7. Example # 11 11. Give the first five terms of the geometric sequence a 1 = 2 r= 3

8. #21 Write the first five terms of the geometric sequence, determine the common ratio and write a n as a function of n a 1 = 64 a k+1 =

9. If r is negative, you will have alternating signs!! #24

10. Determining a Geometric Series In other words, adding the terms of a geometric sequence Two types of sums/ series: 1.) Infinite Geometric Series 2.) Finite Geometric Series

11. The Sum of an Infinite Geometric Series Condition: This can only be done if Notation and how to calculate an INFINITE GEOMETRIC SERIES/ SUM

12. Proof

13. Consider.3 +.03 +.003 …….

14. Why are we able to add an infinite number of terms? Consider (82ish)

15. #78

16. The Sum of a Finite Geometric Series The sum of a finite geometric sequence

17. BEWARE of START INDEX NUMBER 52 vs 60

18. Homework Pg. 640 #1-7; 11-14; 21-24; 28-38(even); 39-42 52- 62(evn); 71- 74; 78-88(even); 91-92; 98; 99; 101