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Chapter 2.3-2.4 “If you do something once, people call it an accident. If you do it twice, they call it a coincidence. But do it a third time and you’ve just proven a natural law.” Grace Murray Hopper Objectives • Generalize basic number patterns to a method for finding the nth term in a linear number sequence. • Apply inductive reasoning to find patterns. • Apply mathematical models to problem solving. Example Find the next term in the sequence 20, 27, 34, 41, 48, 55,……. How did you find it? What is the 200th term in this sequence? How do we find this? Function Rule To find the 200th term of any sequence, we would need to have a rule that would generate that term, or any term we needed. The rule that gives the nth term for a sequence is called the function rule. Investigation Finding the Rule Pg 106 Example Find the rule for the following sequence: Term 1 2 3 4 5 6 …… Value 7 -2 -3 -8 -13 -18 …… n Mathematical Models When you draw graphs or pictures of situations, or when you write equations that describe a problem, you are creating mathematical models. Investigation Party Handshakes Pg 113 Homework Section 2.3 and Section 2.4 Quiz TOMORROW