Transcript 1_7 Patterns and Sequences Notes

1-7
1-7 Patterns
Patternsand
andSequences
Sequences
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
11
1-7 Patterns and Sequences
Warm Up
Determine what could come next.
1.
2.
3.
4.
5.
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3, 4, 5, 6, ___
10, 9, 8, 7, 6, ___
1, 3, 5, 7, ___
2, 4, 6, 8, ___
5, 10, 15, 20, ___
7
5
9
10
25
1-7 Patterns and Sequences
Learn to find patterns and to recognize,
describe, and extend patterns in
sequences.
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1-7 Patterns and Sequences
Vocabulary
perfect square
term
arithmetic sequence
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1-7 Patterns and Sequences
Each month, Eva chooses 3 new DVDs from her
DVD club.
Eva’s DVDs
Position
Month
DVDs
1
2
3
4
3
6
9
12
Value
+3
+3
+3
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, 18, …
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1-7 Patterns and Sequences
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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1-7 Patterns and Sequences
Helpful Hint
Look for a relationship between the 1st term and
the 2nd term. Check if this relationship works
between the 2nd term and the 3rd term, and so
on.
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1-7 Patterns and Sequences
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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1-7 Patterns and Sequences
Additional Example 1B: Extending Arithmetic
Sequences
Position
Value of Term
1
9
2
22
3
35
4
48
5
6
+13 +13 +13 +13 +13
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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1-7 Patterns and Sequences
Check It Out: Example 1A
Identify a pattern in each sequence and name
the next three terms.
39, 34, 29,
–5
–5
–5
24,
–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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1-7 Patterns and Sequences
Additional Example 2A: Completing Other
Sequences
Identify a pattern in the sequence. Name the
missing terms.
24,
34, 31,
+10 –3
41, 38, 48,
+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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1-7 Patterns and Sequences
Additional Example 2B: Completing Other Sequences
Position
1
2
3
4
Value of Term
1
4
2
8
4
÷2
5
6
16
7
8
32
 4 ÷2  4 ÷2  4
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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1-7 Patterns and Sequences
Check It Out: Example 2B
Position
1
2
3
4
Value of Term
1
6
3
18
6
÷2
6
5
6
54
÷2
6
7
8
162
÷2  6
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.
Course 1