1 1 Patterns and Inductive Reasoning Inductive reasoning

1 -1 Patterns and Inductive Reasoning

Inductive reasoning- Reasoning that is based on patterns you observe. EX. Find the pattern for the sequence. Use the pattern to show the next two terms in the sequence. 4, 8, 16, 32 Pattern: Each term is two times the preceding term Next Two Terms? ? ? 64 & 128

EX. Find the pattern for the sequence. Use the pattern to show the next two terms in the sequence. Pattern: Each circle has one more segment through the center to form equal parts. Next Two Terms? ? ?

On your own!!!! State the pattern and the next two terms in the sequence. 1) 1, 2, 4, 7, 11, 16 2) 90º , 135º , 157. 5º

Conjecture a conclusion you reach using inductive reasoning EX. Make a conjecture about the sum of the first 30 odd numbers; Find the first few sums and see if a pattern exists. ALL ARE PERFECT 1 = 1² SQUARES!!!!!! 1+3 = 4 = 2² 1+3+5 = 9 = 1 + 3 + 5 + 7 = 16 = Conjecture: The 3² sum of the first 30 odd numbers 4² will be 30² or 900.

Testing a conjecture Counterexample- an example for which the conjecture is incorrect. EX. Find one counterexample to show that each conjecture is false. 1) The difference of two integers is less than either integer. Counterexample: -6 –(-4)= -2 -2 <-6 -2 <-4

On your own Provide a counterexample to show that each conjecture is false. 1) The product of a positive and negative number is always less than either numbers. 2) The sum of two numbers is greater than either number.