Download 11-2 Arithmetic Sequences Objective:  Identify and generate arithmetic sequences. 11­2 Arithmetic Sequences

11­2 Arithmetic Sequences
April 21, 2009
11-2 Arithmetic Sequences
Objective: Identify and generate arithmetic sequences.
Lesson & Objective
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11­2 Arithmetic Sequences
April 21, 2009
Arithmetic Sequence
An Arithmetic Sequence is a sequence in which the difference between any term and the term before it is constant.
Is the given sequence arithmetic?
1) 2, 4, 8, 16,...
2) 48, 45, 42, 39,...
3) 16, 22, 28, 34,...
4) 2, 5, 7, 12,...
Arithmetic Sequence
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11­2 Arithmetic Sequences
April 21, 2009
Writing an Explicit Formula for an Arithmetic Sequence
Formula for Arithmetic Sequences:
a = a + d(n­1)
1
n
th
n
m
ter
erm
F
T
irst
on e
m
m nc
Co ffere
Di
Arithmetic Sequence
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11­2 Arithmetic Sequences
April 21, 2009
a = a + d(n­1)
n
1
th
n
Example:
m
ter
Fir
st
m
Ter
n
mo ce
m
n
Co ffere
i
D
1, 3, 5, 7, ...
7 ­ 5 = 2
5 ­ 3 = 2
3 ­ 1 = 2
d = 2
a = 1 + 2(n­1)
n
a = 1 + 2n ­ 2 n
a = 2n ­ 1 n
Arithmetic Sequence
4
11­2 Arithmetic Sequences
April 21, 2009
a = a + d(n­1)
n
1
th
n
Example:
m
ter
Fir
st
m
Ter
n
mo ce
m
n
Co ffere
i
D
2, 5, 8, 11 ...
Arithmetic Sequence
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11­2 Arithmetic Sequences
April 21, 2009
Arithmetic Mean
The arithmetic mean of any two numbers is the average of the two numbers.
sum of the two numbers arithmetic mean = 2
For any three sequential terms in an arithmetic sequence, the middle term is the arithmetic mean of the 1st and 3rd terms.
Nov 22 ­ 10:10 AM
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11­2 Arithmetic Sequences
April 21, 2009
For each sequence find the value of x if the sequence is arithmetic.
Ex) 2, x, 10
Ex) 5, x, 25
Nov 22 ­ 10:10 AM
7
11­2 Arithmetic Sequences
April 21, 2009
For each sequence find the value of x if the sequence is arithmetic.
Ex) 84, x, 110
Ex) 24, x, 57
Nov 22 ­ 10:10 AM
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11­2 Arithmetic Sequences
April 21, 2009
Homework
Page: 608
#'s: 2 ­ 30 even,
52 ­ 60 all
Explicit formulas only!!!
Nov 22 ­ 10:10 AM
9