11­1 Mathematical Patterns
April 20, 2009
11.1 Mathematical Patterns
Objective:
Sierpinski Triangle
Write the explicit formula for a given sequence.
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11­1 Mathematical Patterns
April 20, 2009
Check Skills You'll Need Find the next two numbers of each pattern.
How did you find the numbers?
1. 1, 3, 5, 7, 9,...
2. ­2, ­4, ­6, ­8, ­10,...
3. 0.2, 1, 5, 25, 125, 625,...
4. ­3, ­7, ­11, ­15,....
Fractal
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11­1 Mathematical Patterns
April 20, 2009
New Vocabulary:
sequence: an ordered list of numbers
term: each number in a sequence
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11­1 Mathematical Patterns
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Describe each pattern formed. Find the next three terms.
1) 27, 34, 41, 48,...
2) 243, 81, 27, 9,...
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11­1 Mathematical Patterns
April 20, 2009
Match the term with its definition:
n
position number
an
term value based on a specific position number
n + 1
n ­ 1
the next term in the sequence
the previous term in the sequence
Definitions:
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11­1 Mathematical Patterns
April 20, 2009
Explicit formula ­ A formula that gives the value of any term a in terms of n.
n
Translation:
You can find the value of any term in the sequence so long as you
know the position number.
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11­1 Mathematical Patterns
April 20, 2009
Find the term value for the 1st, 3rd and 10th position.
An =
2n ‐ 5
n
A1=
2 (1) ‐ 5
1
A3=
2 (3) ‐ 5
3
A 10 =
2 (10) ‐ 5
10
A1=
2‐5
1
A3=
6‐5
3
A 10 =
20 ‐ 5
10
A3=
1
3
A 10 =
15
10
A1=
‐3
1
A 1 = ‐3
A 10 = 1.5
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11­1 Mathematical Patterns
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th
Find the explicit formula for the n term in the sequence.
position
1
2
5
n
term
3
5
7
9
11
2n + 1
position
1
2
3
4
5
n
term
2
4
8
16
32
2n
3
4
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11­1 Mathematical Patterns
April 20, 2009
th
Find the explicit formula for the n term in the sequence.
position
1
2
3
4
5
n
term
­2
1
4
7
10
3n - 5
position
1
2
3
4
5
n
term
5
3
7
3
2
9
5
(n + 4)
n
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11­1 Mathematical Patterns
April 20, 2009
Homework
Page: 603
#'s: 1-9, 18-23, 47-50
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