“Our character is basically a composite of our habits. Because they are consistent, often unconscious patterns, they constantly, daily,

express our character…”

-Stephen R. Covey

Inductive Reasoning

Inductive reasoning is reasoning based on patterns you observe.

Examples:Find the pattern of the sequence and show the next two terms or symbols.

2, 4, 8, 16, …

1, 3, 7, 13, 21, …

Using Inductive Reasoning

A conjecture is a conclusion you reach using inductive reasoning.

Example:Sum of odd numbers.

11 + 31 + 3 + 51 + 3 + 5 + 7

= 1= 4= 9= 16

= 12

= 22

= 32

= 42

What is the sum of the first 30 odd numbers?

The first 35 odd numbers?Conjecture:

Using Inductive Reasoning

A conjecture is a conclusion you reach using inductive reasoning.

Example:Sum of even numbers.

22 + 42 + 4 + 62 + 4 + 6 + 8

= 2= 6= 12= 20

= 1(1 +1)= 2(2+1)= 3(3+1)= 4(4+1)

What is the sum of the first 30 even numbers?

The first 35 even numbers?Conjecture:

Using Inductive Reasoning

A counterexample to a conjecture is an example where the conjecture does not work.

Example:Find a counterexample to the statements.

“If a number is divisible by 2, then it is also divisible by 6.”

“You can connect any three points to form a triangle.”

1.1 Patterns and Inductive Reasoning1.1 Patterns and Inductive Reasoning

“Our character is basically a composite of our habits. Because they are consistent, often unconscious patterns, they constantly, daily,

express our character…”

-Stephen R. Covey

Practice: Inductive Reasoning WorksheetTerms: inductive reasoning, conjecture, counterexample

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