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11.1 Introduction to Sequences and Series: Day 1 - Sequences Sequence : A collection of numbers listed in order. Domain: Gives the POSITION of each term. If a domain is not specified it is understood to begin with 1. n = 1, n = 2, n = 3, … Range: Gives the TERMS of the sequence as determined by a formula, an . Example: an = 3n2 +1 n = 1, 2, 3, 4, 5 an = 4, 13, 28, 49, 76 Find the first 4 terms of the sequence. 1. an = 2n 2. an = 2n +1 3. an = 2n -1 4. æ 1ö an = ç ÷ è 2ø 5. æ 1ö an = ç - ÷ è 2ø 6. an = n 2 n n Rules For Sequences: Rules for Sequences should be FORMULAS so you can find ANY term in the sequence. Consider the Sequence 3, 6, 9, 12, 15 What is happening each time? General Rule : an Graph the sequence of numbers by graphing the general rule. Domain (which term?) n=1 n=2 n=3 n=4 n=5 Range (value of the term) a1 = 3 a2 = 6 a3 = 9 a4 = 12 a5 = 15 Find the 100th term of the sequence:___________ Writing Rules for your sequences. For each of the below sequences write a general rule for the nth term of the sequence. 1.) 2, 4, 6, 8,... 2.) 2 2 2 2 , , , ,... 5 25 125 625 n: n: an : an : General Rule: an = General Rule: an = 3 4 5 6 , , , ... 2 3 6 7 1 1 1 1 3.) , , , ,... 3 9 27 81 4.) n: n: an : an : General Rule: an = General Rule: an = Graphing Sequences Use your graphing calculator to create graphs of sequences. MODE SEQ DOT ENTER Y= Let nMin = 1 Enter the general rule as u(n) Set a reasonable window GRAPH Create the graph of the sequences listed below. 1. an = n 2 1, 4, 9, 16, 25 2. Homework: p. 655 (9-15 odd, 21-29, 30,32,34,35) an = (-1)n+1 (n) 1, -2, 3, -4, 5, -6