Transcript 4, -12, -36, -108, …and write the next three numbers

GEOMETRY: CHAPTER 1
Ch. 1.1 Use Inductive
Reasoning
Ex. 1
Describe the pattern in the numbers -4,
-12, -36, -108, …and write the next
three numbers in the pattern.
Ex. 1
Describe the pattern in the numbers -4,
-12, -36, -108, …and write the next
three numbers in the pattern.
Notice that each number in the pattern
is three times the previous number
-4, -12, -36, -108, -324, -972, -2916, …
So, the next three numbers in the pattern
are -324, -972, and -2916.
Ex. 2 Describe the pattern in the numbers
4.01, 4.03, 4.05, 4.07, …Write the next
three numbers in the pattern.
Ex. 2 (cont.) Describe the pattern in the
numbers 4.01, 4.03, 4.05, 4.07, …Write
the next three numbers in the pattern.
The numbers are increasing by 0.02. The
next 3 numbers are: 4.09, 4.11, 4.13.
Go to:
http://www.classzone.com/cz/books/geometry_2007_
na/resources/applications/animations/g7_1_1.html
for more questions about number patterns.
Inductive Reasoning
A conjecture is an unproven statement
that is based on observations.
You use inductive reasoning when you
find a pattern in specific cases and then
write a conjecture for the general case.
Ex. 3: Make and Test a Conjecture
Use the following sums of odd integers:
5 + 7 = 12, 1 + 3 = 4, 19 + 23 = 42
CONJECTURE: The sum of any two odd
integers is . . .
To show that this is true, I need to test the
conjecture with other examples.
43 + 33 = 76, 67 + 1=68, 25 + 7 = 32
Disproving Conjectures
To show that a conjecture is true, you
must show that it is true for all cases. You
can show that a conjecture is false,
however, by finding one counterexample.
A counterexample is a specific case
for which the conjecture is false.
Ex. 4. Find a counterexample.
A student makes the following
conjecture that the difference of two
numbers is always less than the
larger number.
Conjecture: the difference of two
numbers is always less than the
larger number.
Ex. 4 (Cont.) Solution
To find a counterexample, you need to find a
difference that is greater than the larger number.
7- (-5) = 12
12 > 7
The difference, 12, is greater than the larger number,
7.
Thus, the conjecture stating that “the difference of
two numbers is always less than the larger
number” is false.
Images used for this presentation came from
the following websites:
http://z.about.com/d/math/1/0/M/2/perpendic
ular.jpg
http://education.yahoo.com/homework_help/
math_help/solutionimages/minigeogt/2/1/1
/minigeogt_2_1_1_25_10/f-10-24-1.gif