2.1 – Use Inductive Reasoning

Inductive Reasoning: Make predictions based on patterns

Conjecture: An unproven statement that is based on observations

Counterexample: A statement that contradicts a conjecture

1. Sketch the next figure in the pattern.

1. Sketch the next figure in the pattern.

3. Describe a pattern in the numbers. Write the next three numbers in the pattern.

5, 10, 15, 20

+5 +5 +5 +5

25, 30, 35

2, 6, 18, 54

x3 x3 x3 x3

162, 486, 1,458

3. Describe a pattern in the numbers. Write the next three numbers in the pattern.

3, -9, 27, -81

x-3 x-3 x-3 x-3

243, -729, 2,187

3. Describe a pattern in the numbers. Write the next three numbers in the pattern.

2, 3, 5, 8, 12

+1 +2 +3 +4 +5

3. Describe a pattern in the numbers. Write the next three numbers in the pattern.

17, 23, 30

2, 5, 11, 23

x2+1 x2+1 x2+1 x2+1

3. Describe a pattern in the numbers. Write the next three numbers in the pattern.

47, 95, 191

1, 1, 2, 3, 5, 8

1+1 1+2 2+3 3+5 5+8

3. Describe a pattern in the numbers. Write the next three numbers in the pattern.

13, 21, 34

# of sides (n)# of diagonalsfrom 1 vertex

3 4 5 6 7 25 n… …

0 1 2 3 4 22 n – 3

1. Make a table displaying the relationship between the number of sides of a shape and the number of diagonals from one vertex. Then make a conjecture for all n-gons.

5. Show the conjecture is false by finding a counterexample.

Any four-sided polygon is a square.

Rectangle

5. Show the conjecture is false by finding a counterexample.

The square root of all even numbers is even.

2 1.414213

HW Problem

# 17

2.1 75-76 1-17 odd, 22

Ans: Example: 25 = 10