Transcript Sequence

Math I
Day 10 (1-19-10)
Today’s Question:
How can we write a function to
represent a sequence?
Standard: MM1A1f: Recognize sequences as functions with domains that are
whole numbers
Sequences
0011 0010 1010 1101 0001 0100 1011
• Everyday a radio station asks a question for
a prize of $150. If the fifth caller does not
answer correctly, the prize money increased
by $150 each day until someone correctly
answers their question.
• Make a list of the prize money for a week
from Monday to Friday if no one gets it
right.
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Contest
0011 0010 1010 1101 0001 0100 1011
Monday: $150
Tuesday: $300
Wednesday: $450
Thursday: $600
Friday: $750
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Sequences
0011 0010 1010 1101 0001 0100 1011
These prize amounts form a sequence.
Sequence: A function whose domain is a set
of consecutive whole numbers.
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What would be the value on Day 6? Day 7?
An Arithmetic Sequence: is a sequence that
has a common number added to every term
Sequences
The values in the range are called the terms
0011 0010 1010 1101 0001 0100 1011
of the sequence.
Domain: 1
2
3
4…....n
Range:
a2
a3
a4….. an
a1
1
2
4
A sequence can be specified by an equation or
rule.
Contest
0011 0010 1010 1101 0001 0100 1011
a1
$150
a2
$300
a3
$450
a4
$600
a5
$750
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an represents a general term where n can be any
number. What is the closed formula for an?
Sequences
0011 0010 1010 1101 0001 0100 1011
Sequences can continue forever. We can
calculate as many terms as we want as long as
we know the rule or equation for an.
Example:
3, 5, 7, 9, ___ , ___,……. _____ .
an = 2n + 1
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Writing Terms of a Sequence
0011 0010 1010 1101 0001 0100 1011
an = 2n – 3
Find a1, a2, a3, a4, a5
a1 = -1
First Term
a2 = 1
Second Term
a3 = 3
Third Term
a4 = 5
Fourth Term
a5 = 7
Fifth Term
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Example 1
0011 0010 1010 1101 0001 0100 1011
an = 2n – 20
Find a1, a2, a3, a4, a5
a1 =
-18
First Term
a2 =
-16
Second Term
a3 =
-14
Third Term
a4 =
-12
Fourth Term
a5 =
-10
Fifth Term
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Recursive rule v. Closed rule
0011 0010 1010 1101 0001 0100 1011
• Recursive rule: relates one term to the
previous term
– How to find:state the first term (t1=?), then state
what operation much occur on that term to get
to the next term (tn=tn-1+d)
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• Closed rule: allows you to calculate any
term in the sequence directly
– How to find: the equation will always have the
form tn=dn+b, where d is the number you added
in the recursive rule, and b is whatever number
will make tn=t1 when n=1
Example 2
0011 0010 1010 1101 0001 0100 1011
a1 = 2
First Term
a2 = 6
Second Term
a3 = 10
Third Term
a4 = 14
Fourth Term
an =
nth Term
What is the recursive rule?
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t1 = ???, tn-1 = ???
t1= 2, tn=tn-1+4
What is the closed rule? tn = ???
tn= 4n - 2
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Example 3
0011 0010 1010 1101 0001 0100 1011
a1 = 5
First Term
a2 = 12
Second Term
a3 = 19
Third Term
a4 = 26
Fourth Term
an =
nth Term
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What is the recursive rule? t1 = ???, tn-1 = ???
t1=5, tn=tn-1+7
What is the closed rule? tn = ???
tn= 7n - 2
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EOCT Practice
a) 771101 0001 0100 1011
0011 0010 1010
c) 84
b) 81
d) 86
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b
EOCT Practice
Find the 25th term of the sequence 7, 11, 15, 19, 23, ...
0011 0010 1010 1101
0001 0100 1011
a) 103
c) 107
b) 104
d) 111
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a