Transcript Arithmetic Sequences

Homework Questions
Number Patterns
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2.
3.
4.
Find the next two terms, state a rule
to describe the pattern.
1, 3, 5, 7, 9…
16, 32, 64…
50, 45, 40, 35…
-3, -7, -11, -15…
Sequence Notation
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A sequence is an ordered list of
numbers – each number is a term.
State the first 5 terms:
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an = n
(plug in 1, 2, 3, 4, 5)
1, 2, 3, 4, 5
More Examples
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2.
an = 4n
4.
6
3
an = 2n-3
5.
3.
an = n
an =
|1-n2|
an =  13
n
Recursive v. Explicit
Definition
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Recursive Formula – a sequence is
recursively defined if the first term is
given and there is a method of
determining the nth tem by using the
terms that precede it.
English – if you can use the term before
it to figure out what comes next
Ex: {-7, -4, -1, 2, 5, …}
Examples of Recursive
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{-9, -4, -2, 0, 2, …}
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{-4, -8, -16, -32, -64, …}
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{6, 11, 16, 21, 26, …}
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{8, 4, 2, 1, …}
Definition
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Explicit Formula – a formula that
allows direct computation for any term
for a sequence
English – you don’t need to term prior
in order to figure out what the nth term
is going to be.
Ex: {8, 9, 10, 11, 12, …}
an= n + 7
Examples of Explicit
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{-3, 1, 5, 9, …}
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{1, 4, 9, 16, …}
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{7, 9, 11, 13, …}
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{24, 20, 16, 12, …}
Arithmetic Sequences
Arithmetic Sequences
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In an arithmetic sequence, the
difference between consecutive terms is
constant.
The difference is called the common
difference.
To find d: 2nd term – 1st term
Arithmetic?
1.
2, 4, 8, 16
2.
6, 12, 18
3.
48, 45, 42
4.
2, 5, 7, 12
Arithmetic Sequence Formulas
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Recursive Formula
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an = an-1 + d
use if you know prior
terms
Explicit Formula
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an = a1 + (n-1)d
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an = nth term
a1 = 1st term
n = number of
terms
d = common
difference
Examples
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Find the 20th term of each sequence
213, 201, 189, 177…
2.
.0023, .0025, .0027…
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More examples
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3.
Find the 17th term of the sequence:
a16 = 18, d = 5
Find the missing term
4.
Use arithmetic mean = average!
84, _______, 110
5.
24, _______, 57
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Homework
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WORKSHEET!
We need to talk about numbers 16-20
though, so wait on me!