Download GEOMETRY 2.1 Patterns and Inductive Reasoning

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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 ____________