Section 1.2

Science
EXAMPLE 1 Make a Conjecture
Complete the conjecture.
Conjecture: The sum of any two odd numbers is __?__.
Solution
Begin by writing several examples.
1 1 2 5 1 6 3 7 10
3 13 16 21 9 30 101 235 336
Each sum is even. You can make the following conjecture.
ANSWER
The sum of any two odd numbers is even.
SCIENTISTS use inductive
reasoning as part of the
scientific method. They
make observations, look for
patterns, and develop
conjectures (hypotheses) that
can be tested.
EXAMPLE 2 Make a Conjecture
Complete the conjecture.
Conjecture: The sum of the first n odd positive integers is __?__.
Solution
List some examples and look for a pattern.
1 1 3 1 3 5 1 3 5 7
1 1 2 4 2 2 9 3 2 16 4 2
ANSWER The sum of the first n odd positive integers is n 2 .
Make a Conjecture
Student Help
READING TIP
Recall that the symbols
and p are two ways
of expressing
multiplication.
Complete the conjecture based on the pattern in the examples.
1. Conjecture: The product of any two odd numbers is __?__.
EXAMPLES
1 1 1 3 5 15 3 11 33
7 9 63 11 11 121 1 15 15
2. Conjecture: The product of the numbers (n 1) and (n 1) is __?__.
EXAMPLES
1 p 3 2 2 1 3 p 5 4 2 1 5 p 7 6 2 1
7 p 9 8 2 1 9 p 11 10 2 1 11 p 13 12 2 1
1.2 Inductive Reasoning 9