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1-1 Patterns and 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.

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1-1 Patterns and Inductive Reasoning

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  1. 1-1 Patterns and Inductive Reasoning

  2. 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

  3. 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?????

  4. On your own!!!!!!!! State the pattern and the next two terms in the sequence. • 1,2,4,7,11,16 , , 90º 135º 157.5º

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

  6. 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 <-4 -2 <-6

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

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