Name____________________________ Date_______
INDUCTIVE REASONING
Inductive Reasoning--- sometimes called inductive logic, is the process to make a generalization on a
few recurring patterns or observations. An inductive pattern can be proven wrong with a
counterexample:
Conjecture: The sum of two number is always greater than the larger number.
Counterexample: −5 + 2 = −3.
1.1 Number patterns
Use inductive reasoning to find the next two terms.
1) 2, 20, 200, 2000,
2) 2, 5, 10, 17, 26, 37,
3) a, 6, c, 12, e, 18,
4) 1, 4, 9, 16, 25,
5) 0, 10, 21, 33, 46,
6) 3, 5, 11, 29, 83, 245
7) Fill in the blank to complete the pattern.
6  7  42
90 1  1
66  67  4422
9  1  2  11
a) 666  667  444222
b) 9  2  3  21
6666  6667  44442222
9  3  4  ___
____ _____  _________
9  ___  5  41
1.2 Verbal patterns
1. Brenda has just gotten a job as the plumber’s assistant. Her first task is to open all the water
valves to release the pressure on the lines. The first four valves she discovered opened when turning
counterclockwise.
a) What is her conjecture?
b) Is this a good example of inductive reasoning?
c) What counterexample would disprove her conjecture?
1
2. Wile E. Coyote is setting up a trap for the roadrunner. Every previous trap has destroyed some
part of his body. However, after he blows himself up he seems to be healed by the next scene.
a) What are two possible conjectures?
b) Is this a good example of inductive reasoning?
c) What counterexample would disprove your conjectures?
3. Ralfy noticed that of the last four days he ate bacon for breakfast Lisa ran from him. Ralfy
concluded that if he had cereal for breakfast, then Lisa would not run from him.
a) Is this a good example of inductive reasoning? Why?
b) What would be a good conjecture based on the description?
1.3 Picture patterns
1) Describe the next picture in the pattern
a)
b)
c)
d)
2