UNIT 11: STATISTICS, SEQUENCES & SERIES
MA40: ALGEBRA II
11.5 – Intro to Sequences & Series
(Text Ref: Ch 11.1, Pg 651-658)
Standards: MA40-S3C1-01,05
Objective: TSWD analysis of sequences/series by discovering the relationship between a set of numbers
and expressing that relationship as a sequence/series.
SEQUENCE
I.
A.
Sequence
Sequence –
Term –
Term
Infinite Sequence –
Infinite Sequence
Finite Sequence –
Finite Sequence
B.
Examples
of Sequences
SEQUENCE
Vocabulary
Examples of Sequences
1. 3, 6, 9, 12, 15
rule: an 
2. -2, -1, 0, 1, 2, 3
3.
rule: an 
1 2 3 4
, , ,
4 8 12 16
rule: an 
C.
Finding Terms of a Sequence
Find the first four terms of the sequences given by
n 1
a. an  2n  3
b. an   2
D.
WRITING About Math – Consider example C-2 above, what do you notice
about the sequence? Why does this happen?
E.
Finding the nth Term of a Sequence
For each infinite sequence, describe the pattern, write the next
term, and write a rule for the nth term.
Finding Terms of
a Sequence
WRITING About Math
Finding the nth Term
of a Sequence
a. 2, 6, 12, 20, . . .
1 1 1 1
b.  , , , ,
3 9 27 81
1
11.5 – Intro to Sequences & Series (continued)
SERIES
Vocabulary
II.
A.
Series –
Series
Finite Series –
Finite Series
Infinite Series
Definition of
Summation Notation
Write Series using
Summation Notation
Using
Summation Notation
SERIES
Vocabulary
Infinite Series –
B.
Definition of Summation Notation
The sum of the first n terms of a sequence is represented
C.
Write each series with summation notation
1. 5  10  15    100
D.
2.  2  4  6    20
Using Summation Notation
Find the sum of the series
6
2.
i 1
E.
k 3
n
n
1 
b.
i 1
F.
2
Formulas for Special Series
1.
Using
Special Formulas
 2  k 
6
 2i
1.
Formulas for
Special Series
3. 1  4  9  16  
n
i 
c.
i
2

i 1
i 1
Using a formula for a sum
10
1.
i
i 1
2

7
2.
i 
i 1
2