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Secondary I Worksheet T1-04, Inductive Reasoning
Name: ______________________________________ Date: _____________ Period: _______
Vocabulary
Inductive Reasoning:
1. Your math teacher has given your class a homework assignment every Monday for the last three weeks.
a. Using inductive reasoning, what could you conclude?
What counterexample would show that your conclusion is false?
b.
2. Every time you ride the bus for the first two weeks of school you notice that
the girls sit on the right side of the bus and the boys sit on the left side.
a. Using inductive reasoning, what could you conclude?
b. What counterexample would show that your conclusion is false?
3. Use the table and inductive reasoning. Make a conjecture about each value.
a. The sum of the first 6 positive even numbers
2
2+4
2+4+6
2+4+6+8
2+4+6+8+10
b. The sum of the first 30 positive even numbers
c. the sum of the first 100 positive even numbers
Use inductive reasoning to find the next two terms in each sequence.
4.)
4, 8, 12, 16, _____, _____
5.)
400, 200, 100, 50, 25, _____, _____
6.)
1/8, 2/7, 1/2, 4/5, _____, _____
7.)
-5, 3, -2, 1, -1, 0, _____, _____
8.)
360, 180, 120, 90, _____, _____
9.)
1, 3, 9, 27, 81, _____, _____
10.)
1, 5, 17, 53, 161, _____, _____
11.)
1, 5, 14, 30, 55, _____, _____
=2
=6
=12
=20
=30
=1●2
=2●3
=3●4
=4●5
=5●6
Draw the next two shapes in each sequence.
12.)
13.)
14.)
15.)
1
4
9
16.)
17). Decide whether each statement is true or false. If false, provide a counterexample.
a. A natural number is also a whole number. [ True or False ]
b. Any integer is a whole number. [ True or False ]
c. Every rational number is also an integer. [ True or False ]
d. Every integer is a rational number. [ True or False ]
e. Every natural number is a whole number, integer, and a rational number. [True or False]
f.
Every whole number is a natural number, integer, and a rational number. [True or False]