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Math II
UNIT QUESTION: How is a
geometric sequence like an
exponential function?
Standard: MM2A2, MM2A3
Today’s Question:
How do you recognize and write
rules for number patterns?
Standard: MM2A3d
Section 4.7
Sequences
&
Series
Sequence
A sequence is a set of numbers
in a specific order
Infinite sequence
Finite sequence
a1 , a2 , a3 , a4 ,..., an ,...
a1 , a2 , a3 , a4 ,..., an
Sequences –
sets of numbers
Notation:
an   represents the formula for finding terms 
n  term number
a4 is the notation for the 4th term
a32 is the notation for the 32nd term
Examples:
If an  2n  3, find the first 5 terms.
If an  3n  1, find the 20th term.
.
Ex 1
Find the first four terms of the sequence
an  3n  2
a1  3(1)  2  1
First term
a2  4
Second term
a3  7
Third term
a4  10
Fourth term
Ex. 2
Find the first four terms of the sequence
(1)
an 
2n  1
n
Writing Rules for Sequences
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
Writing Rules for Sequences
Try these!!!
3, 6, 9, 12, ___ , ___,……. _____ .
1/1, 1/3, 1/5, 1/7, ___ , ___,……. _____ .
an = 3n, an = 1/(2n-1)
Series –
the sum of a certain
number of terms of a sequence
n
Sigma Notation :
a
i 1
Stop
Formula
i
Start
“Add up the terms in the sequence
beginning at term number 1 and going
through term number “n”.
4
1.  -5i  5 1  5  2  5  3  5  4  50
i 1
5
2. 
i 1
7
1
2
3.  i
i3
6
4.
3
i 1
25
i 1 
2
 25
Infinite Sequence
a1 , a2 , a3 , a4 ,..., ai ,...

Infinite Series
a1  a2  a3  a4  ...  ai  ...   ai
i 1
Finite Series or nth Partial Sum
n
a1  a2  a3  a4  ...  an   ai
i 1
SUMMATION NOTATION
Sum of the terms of a finite sequence
Upper limit of summation
(Ending point)
n
a
i 1
i

Lower limit of summation
(Starting point)
5
 3i
Ex 7
i 1
 45
If you have a constant you can pull it out in front FIRST
5
 3i
i 1
5
 3 i
i 1
Ex 7b
6
 (1  k
k 3
2
)  (1  3 )  (1  4 )  (1  5 )  (1  6 )
 (10)  (17)  (26)  (37)
 90
2
2
2
2
Homework
Page 135 #2-16 (even), 22-24, 26