Exploring Patterns and Inductive Reasoning

What is inductive reasoning based on?

• Hypotheses

• Experiments

• Patterns

• Logical deduction

In the sequence 3, 9, 27, 81, what is the pattern?

• Dividing by 3

• Subtracting 3

• Multiplying by 3

• Adding 6

What shape comes next in the pattern: circle with a triangle, circle with a square, circle with a pentagon?

• Circle with a nonagon

• Circle with a hexagon

• Circle with a heptagon

• Circle with an octagon

What is a conjecture?

• An unproven statement based on observation

• A mathematical theorem

• A proven statement

• A random guess

What is the sum of the first three odd positive integers?

• 15

• 9

• 6

• 12

What is the 21st term in the repeating pattern RWB?

• R

• None of the above

• W

• B

What is a counterexample?

• An example that proves a conjecture

• A hypothetical example

• An example that disproves a conjecture

• A random example

Which of the following is a counterexample to the conjecture: 'For all real numbers x, x^2 is greater than or equal to x'?

• x = 0.5

• x = -1

• x = 2

• x = 1

What happens when you multiply a negative number by 2?

• The product is always zero

• The product is always greater than the original number

• The product is always less than the original number

• The product is always positive

Why is inductive reasoning important in mathematics?

• It is used in logical deductions

• It helps in proving theorems

• It helps in finding patterns and making conjectures

• It is used in experiments