1. Sequences & Series Pre-Calculus Lesson 9.1

2. Infinite Sequence: A sequence without bound - - 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … ? (what’s next 2 terms)

3. We use the letter, a, with a subscript to represent function values of a sequence. 1, 1, 2, 3, 5, 8…. a 1 = 1 a 2 = 1 a 3 = 2 a 4 = 3 a 5 = 5 a 6 = 8

4. Finite Sequence: Find the first n terms only. a n represents the nth term of a sequence…. The entire sequence is represented by a n

6. [2 nd ] [Stat]  OPS #5[Seq] Seq (function, variable, first term, last term) Hit the right arrow key if all values are not visible. SEQUENCES IN YOUR CALCULATOR OR…. Change the mode on calculator to seq Plug in equation beside u(n) Graph Use trace to toggle through values

7. A recursion formula defines the nth term (a n ) of a sequence as a function of the previous term (a n-1 ) 4. Find the first four terms of the sequence where a 1 = 5 and a n = 3a n-1 + 2, where n>2. 5. Find the first four terms of the sequence where a 1 = 3 and a n = 2a n-1 + 5, where n>2.

8. Factorial Notation Products of consecutive positive integers; the integers decrease by one….. Example: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 6. 2 ∙ 3!7. (2 ∙ 3)!

10. [Math]  PRB #4 [!}

11. Summation Notation Compact notation for expressing the first n sums of a sequence a 1 + a 2 + a 3 +… a n = 11. 12.

12. Expand and evaluate. 13. 14.

13. [2 ND ] [Stat]  Math #5 [sum] Then enter sequence… Sum(seq(function, variable, first term, last term)) Summations in your calculator

14. Express each sum using summation notation. 15. 1 3 + 2 3 + 3 3 + … + 7 3 16. 2 3 + 2 4 + … + 2 7

15. Properties of Sums

16. Many applications involve the sum of an infinite sequence. Such a sum is called a series. To find the sum of a series, you would notice and extending pattern… 17. Find the third partial sum and the sum of