Download 2-1: Patterns and Inductive Reasoning 45, 40, 35, 30,... 25, 20

2-1: Patterns and Inductive
Reasoning
What are the next two terms in each sequence?
a. 45, 40,35,30,...
25, 20
b.

Inductive Reasoning
◦ Based on observed patterns

Conjecture
◦ Conclusion reached using inductive reasoning
◦ Used when can’t find every pervious term
1
What conjecture can you make about the number of
regions 20 diameters form? 20  2  40 regions
1 diameter forms 2 regions
2 diameters form 4 regions
3 diameters form 6 regions
5 diameters form 10 regions
Complete Got It? #2 p. 83 B; Every 3rd term is B so the 21st term will be B
Collecting Information and Making a Conjecture
What conjecture can you make about the sum of the
first 30 even numbers?
Number of Terms
Sum
 1 2 
1
2
2
2
3
24
246
2 468
 6  2  3
 12  3  4 
4
 20  4  5 
You multiply the term number by one number higher.
So the sum of the 1st 30 terms is: 30  31  930
Complete Got It? #3 p. 83
302 = 900
2
Making a Prediction
Sales of tickets at an amusement park increased over a
period of four consecutive months. What conjecture can
you make about the number of tickets the park will sell in
February?
What amount does
the ticket sales change
by? About 100 tickets
The amusement park
will sell about 500
tickets in February.
60
600
50
500
40
400
30
300
20
200
Complete Got It? #4
p. 84
10
100
a. About 7500
b. No
O
N
D
J
F5
M
Testing Conjectures

Counterexample
◦ Example proving conjecture false
◦ Only need one
Give a counterexample for each conjecture:
1) If an animal is green, it is a frog. An alligator
2) Any three segments form a triangle.
3, 4, 8
3) When you multiply a number by 2, the product is
divisible by 4. 3x2=6
Complete Got It? #5 p. 84
3
Homework: p. 85 #7-37 odd, 54, 62-64
4