Page 747 - Basic College Mathematics with Early Integers

Appendix

Inductive and Deductive
C

Reasoning

Logic and logical reasoning have applications in many fields, including science, law, Objectives
psychology, and mathematics. For example, computers must have logic built into
their circuits in order to process information correctly. We begin our study of logic Understand and Use Inductive
by examining inductive reasoning. Reasoning.

Understand and Use Deductive
Reasoning.
Objective Using Inductive Reasoning

Inductive Reasoning
This is the process of forming a general conclusion based on observing a num-
ber of specific examples or outcomes.
leads to a
Specific Observations : general conclusion

Example 1 Find the next number in the sequence, or listing, of numbers. PRACTICE 1
Find the next number in the
1, 5, 25, 125
sequence
Solution: Each number after the first is obtained by multiplying the previous 2, 6, 18, 54
number by 5. If we assume that this pattern continues, the next number is
125 * 5 = 625 .

1, 5, 25, 125, 625
R Q R Q R Q R Q
#
#
#
#
1 5 5 5 25 5 125 5
Work Practice 1
Example 2 Find the next two numbers in the given sequence. PRACTICE 2
Find the next two numbers in
1, 1, 2, 3, 5, 8
the sequence
Solution: Each number after the first two numbers is obtained by adding the 2, 4, 6, 10, 16
two previous numbers in the list. Notice that 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5,
and so on. If this pattern is to continue, the next number in the sequence is
5 + 8 = 13 , and the next number is 8 + 13 = 21 .
Work Practice 2

The sequence described in Example 2 is called the Fibonacci sequence. There are
many examples of this sequence found in nature. This sequence also has many
applications including those in science, business, economics, operations research,
archeology, fine arts, architecture, and poetry. Answers
1. 162 2. 26, 42
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