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2-1: Patterns and Inductive Reasoning What are the next two terms in each sequence? a. 45, 40,35,30,... 25, 20 b. Inductive Reasoning ◦ Based on observed patterns Conjecture ◦ Conclusion reached using inductive reasoning ◦ Used when can’t find every pervious term 1 What conjecture can you make about the number of regions 20 diameters form? 20 2 40 regions 1 diameter forms 2 regions 2 diameters form 4 regions 3 diameters form 6 regions 5 diameters form 10 regions Complete Got It? #2 p. 83 B; Every 3rd term is B so the 21st term will be B Collecting Information and Making a Conjecture What conjecture can you make about the sum of the first 30 even numbers? Number of Terms Sum 1 2 1 2 2 2 3 24 246 2 468 6 2 3 12 3 4 4 20 4 5 You multiply the term number by one number higher. So the sum of the 1st 30 terms is: 30 31 930 Complete Got It? #3 p. 83 302 = 900 2 Making a Prediction Sales of tickets at an amusement park increased over a period of four consecutive months. What conjecture can you make about the number of tickets the park will sell in February? What amount does the ticket sales change by? About 100 tickets The amusement park will sell about 500 tickets in February. 60 600 50 500 40 400 30 300 20 200 Complete Got It? #4 p. 84 10 100 a. About 7500 b. No O N D J F5 M Testing Conjectures Counterexample ◦ Example proving conjecture false ◦ Only need one Give a counterexample for each conjecture: 1) If an animal is green, it is a frog. An alligator 2) Any three segments form a triangle. 3, 4, 8 3) When you multiply a number by 2, the product is divisible by 4. 3x2=6 Complete Got It? #5 p. 84 3 Homework: p. 85 #7-37 odd, 54, 62-64 4