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1. Opener a) Draw a chord, a tangent, and a secant. What are the next two terms?

Inductive Reasoning and Finding nth Term. 1. Opener a) Draw a chord, a tangent, and a secant. What are the next two terms? b) 4, 6, 2, 8, 0, 10, ... , c) F, M, A, M, J, J, ... , d) How many diagonals does an octagon have? e) What percent of people regret getting their tattoos?.

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1. Opener a) Draw a chord, a tangent, and a secant. What are the next two terms?

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  1. Inductive Reasoning and Finding nth Term 1. Opener a) Draw a chord, a tangent, and a secant. What are the next two terms? b) 4, 6, 2, 8, 0, 10, ... , c) F, M, A, M, J, J, ... , d) How many diagonals does an octagon have? e) What percent of people regret getting their tattoos?

  2. 2. Investigation: Finding the Rule

  3. Inductive Reasoning Most learning occurs through inductive reasoning, making generalizations from observed patterns in data.

  4. Everyday Conjectures • If I flip the light switch up, then … the light will turn on. • If I touch the stove while it’s on, then … I will burn my hand. • If then…

  5. EXAMPLE A A scientist dips a platinum wire into a solution containing salt (sodium chloride), passes the wire over a flame, and observes that it produces an orange-yellow flame. She does this with many other solutions that contain salt, finding that they all produce an orange-yellow flame. Make a conjecture based on her findings. “If a solution contains sodium chloride, then in a flame test it produces an orange-yellow flame.

  6. EXAMPLE B Consider the sequence 2, 4, 7, 11 … Make a conjecture about the rule for generating the sequence. Then find the next three terms. If the pattern continues, then you always add the next counting number to get the next term.

  7. 3. Classwork: Find the function rule f(n) for each sequence. Then find the 20th term in the sequence.

  8. 3. Classwork: Find the function rule f(n) for each sequence. Then find the 20th term in the sequence.

  9. 4. Classwork: Find the rule for the nth figure. Then find the number of colored tilesor matchsticks in the 200th figure.

  10. 5. Homework: 1. 1 Finding the n-Rule

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