1. 1.2 Reasoning Mathematically Two Types of Reasoning Remember to Silence Your Cell Phone and Put It in Your Bag!

2. Inductive Reasoning The process of reasoning from specific facts or instances to a general conclusion specific instances  use observations  conclusion

3. Terminology Conjecture A statement that has not been proved to be true nor shown to be false Generalization A statement that expresses some relationship that is true for all numbers in a specified set Counterexample An example that shows a statement to be false

4. Procedure for Using the Inductive Reasoning Process 1. Check several examples for a possible relationship. 2. Observe that the relationship is true for every example you checked. 3. Conclude that the relationship is probably true for all other examples and state a generalization. 4. Attempt to prove your generalization using deductive reasoning.

5. Sequences A pattern involving an ordered arrangement of numbers, geometric figures, letters, or other entities is called a sequence. Each member of the sequence is called a term of the sequence.

6. Arithmetic Sequence A numerical sequence in which each term is obtained from the previous term by adding a fixed number is called an arithmetic sequence. The fixed number is called the common difference, d.

7. Geometric Sequence A numerical sequence in which each term is obtained from the previous term by multiplying by a fixed number is called a geometric sequence. The fixed number is called the common ratio, r.

8. Fibonacci Sequences The Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13,... A Fibonacci Type Sequence a, b, a+b, a+2b, 2a+3b, 3a + 5b,... Examples: 2, 4, 6, 10, 16, 26,... 1, 3, 4, 7, 11, 18, 29,...

9. Additional Terminology Column Extension Pattern Row Relationship Pattern

10. Deductive Reasoning The process of reasoning from the general to a specific conclusion using rules of logic premises  Use definitions properties axioms theorems  conclusion

11. Omit You may omit pp. 24-35 You will study this in Math 4161!