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2.1 – Use Inductive Reasoning
Inductive Reasoning: Make predictions based
on patterns
Conjecture: An unproven statement that is based
on observations
Counterexample: A statement that contradicts a
conjecture
1. Sketch the next figure in the pattern.
1. Sketch the next figure in the pattern.
3. Describe a pattern in the numbers. Write the next
three numbers in the pattern.
5,
10,
+5
15,
+5
25, 30, 35
20
+5
+5
3. Describe a pattern in the numbers. Write the next
three numbers in the pattern.
2,
6,
x3
18,
x3
54
x3
162, 486, 1,458
x3
3. Describe a pattern in the numbers. Write the next
three numbers in the pattern.
3,
-9,
x-3
27,
x-3
-81 243, -729, 2,187
x-3
x-3
3. Describe a pattern in the numbers. Write the next
three numbers in the pattern.
2,
3,
+1
5,
+2
8,
+3
12
+4
17, 23, 30
+5
3. Describe a pattern in the numbers. Write the next
three numbers in the pattern.
2,
5,
11,
23
47, 95, 191
x2+1 x2+1 x2+1 x2+1
3. Describe a pattern in the numbers. Write the next
three numbers in the pattern.
1,
1,
2,
1+1
3,
1+2
5,
2+3
8
3+5
13, 21, 34
5+8
3. Describe a pattern in the numbers. Write the next
three numbers in the pattern.
3,
0,
-3
-6, … -9, -12, -15
-3,
-3
-3
-3
3. Describe a pattern in the numbers. Write the next
three numbers in the pattern.
288, 144, 72,
36, … 18, 9, 9
2
2
2
2
2
3. Describe a pattern in the numbers. Write the next
three numbers in the pattern.
–1
8
,
1
7
,
2
+1
6
,
3
4 3 2
5
,... 5 , 6 , 7
4
4. Show the conjecture is false by finding a
counterexample.
Any four-sided polygon is a square.
Rectangle
4. Show the conjecture is false by finding a
counterexample.
The square root of a whole number x is always
smaller than the number x
1
1
4. Show the conjecture is false by finding a
counterexample.
For any numbers x and y, where x  0,
x y
y
x
23
3
2
5
3
2
5. Use inductive reasoning to make a conclusion based on the
following:
odd
The product of any two odd numbers is _________.
Ex. 3  3 = 9
Ex. -1  5 = -5
Ex. 7  -9 = -63
6. Suppose you are studying bacteria in biology class.
The table shows the number of bacteria after n
doubling periods. Your teacher asks you to predict
the number of bacteria after 7 doubling periods.
What would your prediction be?
6 7
256 512
x2 x2 x2 x2 x2 x2 x2
7. John believes that his walking speed influences his
heart rate. He took several pulse measurements
based on walking speed and found a line to match his
data.
a. What would you
predict his heart rate
would be if his
walking speed was
2.5mph?
106
7. John believes that his walking speed influences his
heart rate. He took several pulse measurements
based on walking speed and found a line to match his
data.
b. What speed is he
walking if his pulse
rate is 130?
4.0
HW Problem
2.1
75-76 1-17 odd, 22
# 17
Ans: Example: 25 = 10