Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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Warm Up Determine what could come next. 1. 3,
4, 5, 6, ___ 2. 10, 9, 8, 7, 6, ___ 3. 1, 3, 5,
7, ___ 4. 2, 4, 6, 8, ___ 5. 5, 10, 15, 20, ___
7
5
9
10
25
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Problem of the Day How can you place the numbers
1 through 6 in the circles so that the sums along
each side are equal?
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1
2
4
5
3
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Learn to find patterns and to recognize,
describe, and extend patterns in sequences.
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Vocabulary
sequence term arithmetic sequence
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Each month, Eva chooses 3 new DVDs from her DVD
club.
Evas DVDs Evas DVDs
Month DVDs
1 3
2
3
4
Position
Value
6
9
12
The number of DVDs Eva has after each month shows
a pattern Add 3. This pattern can be written as
a sequence. 3, 6, 9, 12, 15,
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A sequence is an ordered set of numbers. Each
number in the sequence is called a term. In this
sequence, the first term is 3, the second term is
6, and the third term is 9.
When the terms of a sequence change by the same
amount each time, the sequence is an arithmetic
sequence.
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Additional Example 1A Extending Arithmetic
Sequences Identify a pattern in each sequence and
then find the missing terms. 48, 42, 36,
30, , , , . . .
6 6 6 6 6 6
Look for a pattern. A pattern is to subtract 6
from each term to get the next term.
30 6 24 24 6 18 18 6 12
So 24, 18, and 12 will be the next three terms.
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Additional Example 1B Extending Arithmetic
Sequences
Position 1 2 3 4 5 6
Value of Term 9 22 35 48
A pattern is to add 13 to each term to get the
next term.
48 13 61 61 13 74
So 61 and 74 will be the next terms in the
arithmetic sequence.
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Check It Out Example 1A Identify a pattern in
each sequence and name the next three terms.
39, 34, 29, 24, , , , . . .
5 5 5 5 5 5
Look for a pattern. A pattern is to subtract 5
from each term to get the next term.
24 5 19 19 5 14 14 5 9
So 19, 14, and 9 will be the next three terms.
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Check It Out Example 1B
Position 1 2 3 4 5 6
Value of Term 7 16 25 34
A pattern is to add 9 to each term to get the
next term.
34 9 43 43 9 52
So 43 and 52 will be the next terms in the
arithmetic sequence.
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Not all sequences are arithmetic sequences.
In nonarithmetic sequences, look for patterns
that involve multiplication or division. Some
sequences may even be combinations or different
operations.
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Additional Example 2A Completing Other
Sequences Identify a pattern in the sequence.
Name the missing terms. 24, 34, 31,
41, 38, 48, , , ,
10 3 10 3 10 3 10 3
A pattern is to add 10 to one term and subtract 3
from the next.
48 3 45 45 10 55 55 3 52
So 45, 55, and 52 are the missing terms.
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Additional Example 2B Completing Other Sequences
Position 1 2 3 4 5 6 7 8
Value of Term 1 4 2 8 16 32
A pattern is to multiply one term by 4 and divide
the next by 2.
8 2 4 4 ? 4 16 16 2 8 8 ? 4 32
So 4 and 8 will be the missing terms in the
sequence.
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Check It Out Example 2A Identify a pattern in
each sequence and name the missing terms.
6, 12, 14, 28 , 30, , ,. . .

? 2 2 ? 2 2 ? 2 2
A pattern is to multiply one term by 2 and add 2
to the next.
30 ? 2 60 60 2 62
So 60 and 62 are the missing terms.
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Check It Out Example 2B
Position 1 2 3 4 5 6 7 8
Value of Term 1 6 3 18 54 162
A pattern is to multiply one term by 6 and divide
the next by 2.
18 2 9 9 ? 6 54 54 2 27 27 ? 6
162
So 9 and 27 will be the missing terms in the
sequence.
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz
Identify a pattern in each sequence, and then
find the missing terms. 1. 12, 24, 36, 48, , ,
, 2. 75, 71, 67, 63, , ,
, Identify a pattern in each sequence. Name the
missing terms. 3. 1000, 500, , 125, 4. 100,
50, 200, , 400, ,
add 12 60, 72, 84
subtract 4 59, 55, 51
divide by 2 250
divide by 2 and multiply by 4 100, 200
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Lesson Quiz for Student Response Systems
1. Identify the missing terms in the sequence.
14, 28, 42, 56, __ , __ , __ , ... A. 70, 84, 98
B. 69, 82, 95 C. 68, 80, 92 D. 67, 78, 89
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Lesson Quiz for Student Response Systems
2. Identify the missing terms in the
sequence. 65, 62, 59, 56, __ , __ , __ , ... A.
51, 46, 41 B. 52, 48, 44 C. 53, 50, 47 D. 54,
52, 50
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Lesson Quiz for Student Response Systems
3. Identify the missing term in the
sequence. 2500, 500, __ , 20, ... A. 100 B. 90
C. 80 D. 70
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Lesson Quiz for Student Response Systems
4. Identify the missing terms in the
sequence. 300, 100, 600,__ , 1200, __ ... A.
200, 300 B. 200, 400 C. 300, 600 D. 300, 800