1. The document provides examples of identifying patterns in sequences and numbers. It discusses using inductive and deductive reasoning to make conjectures about patterns and find counterexamples. 2. The objectives are to find the next term in given sequences, provide counterexamples to disprove statements, and draw conclusions from given information using deductive reasoning. 3. Examples are given of identifying the next terms in patterns like months of the year, multiples of numbers, and progressively smaller decimal values. Inductive reasoning is used to form conjectures about continuing patterns while deductive reasoning draws conclusions from given facts.

1. GT Geometry Drill10/3/13
1. What are the next two terms in the
sequence?
1, 4, 9, 16...
2. Write a counterexample for the following
statement:
For any number m, 3m is odd.

2. Accept the two statements as given
information. State the conclusion based on
the information.
• 1. AB is longer than BC; BC is
longer than CD
• 2. 12 is greater than integer M.
M is greater than 8
• 3. 4x + 6 = 14, then x =?

3. Use inductive and deductive reasoning
to identify patterns and make
conjectures.
Find counterexamples to disprove
conjectures.
Objectives

4. Find the next item in the pattern.
Example 1A: Identifying a Pattern
January, March, May, ...
The next month is July.
Alternating months of the year make up the pattern.

5. Find the next item in the pattern.
Example 1B: Identifying a Pattern
7, 14, 21, 28, …
The next multiple is 35.
Multiples of 7 make up the pattern.

6. Find the next item in the pattern.
Example 1C: Identifying a Pattern
In this pattern, the figure rotates 90° counter-
clockwise each time.
The next figure is .

7. Check It Out! Example 1
Find the next item in the pattern 0.4, 0.04, 0.004, …
When reading the pattern from left to right, the next
item in the pattern has one more zero after the
decimal point.
The next item would have 3 zeros after the decimal
point, or 0.0004.

8. When several examples form a pattern
and you assume the pattern will continue,
you are applying inductive reasoning.
Inductive reasoning is the process of
reasoning that a rule or statement is true
because specific cases are true. You may
use inductive reasoning to draw a
conclusion from a pattern. A statement
you believe to be true based on inductive
reasoning is called a conjecture.

9. Deductive reasoning is the process of using
logic to draw conclusions from given facts,
definitions, and properties.