1. SFM Productions Presents: Another action-packet episode of “Adventures inPre-Calculus!” 9.1Sequences and Series

2. Homework for section 9.1 p647Part 1:19-35, 47-73 (EOO if too much) Part 2:77-119 (EOO if too much)

3. A sequence is a function whose domain is the set of positive integers....... Finite Sequence: domain consists of the first n positive integers.

4. Sometimes can start with a subscript of 0… a 0, a 1, a 2., a 3 … Finding terms of a sequence:

5. There may be more than one pattern that works, but we are only after the most apparent term… Find the n th term: (that means find the formula, or model…… a n = some formula) n anan

6. n anan

7. n anan

8. n anan

9. Some sequences are defined recursively, which means you need to be given one or more of the first term(s) - then the following terms can be found using the previous ones. Recursive sequences use: a k Given: Find the next 4 terms…

10. Given: Find the next 4 terms… We want a 2. And since recursive sequences have the form: a k, that means k = 2. 2 3 5 8 You’re set to do up through problem 59.

11. Another type of sequence is defined as: ! ! = factorialIf n is an integer, then n! is defined as:

12. Evaluating factorials: You’re set to do up through problem 83.

13. Summation Notation:a convenient way to notate the sum of the terms of a finite sequence. Also known as Sigma notation.

14. Find the sum of the first 6 terms (starting with 1) of the sequence: 3n - 1.

15. Break out your battery operated brain…

17. Properties of Sums of sequences:

18. Infinite series Finite series (also called the nth partial sum)

19. 1. Find the 3 rd partial sum. 2. Find the sum of the whole thing…

20. 1. Find the 3 rd partial sum. 2. Find the sum of the whole thing…

21. Go! Do!