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Transcript

2.1 GEOMETRY Patterns and Inductive Reasoning Example: Complete the pattern and give the rule to get to the next number. (1) 1, 4, 16, 64,… (2) -5, -2, 4, 13,… Inductive Reasoning – Conjecture – Example: The sum of the first n odd integers is _________? Counterexample – Example that shows a ____________________ is false. Example: For all numbers x, the expression x. Examples – State the next number in the pattern and give the rule that was used. (1) 1, 4, 7, 10, … (2) 7, 9, 13, 19, 27, … (3) 3, 18, 108, 648, … (4) 4, 6, 9, 13.5, 20.25, … ______________________________________________________________________________ Complete the conjecture (1) The sum of any two odd numbers is ____________ (2) The product of any two odd numbers is ____________