11.1 Introduction to Sequences and Series: Day 1 - Sequences
Sequence : A collection of numbers listed in order.
Domain: Gives the POSITION of each term. If a domain is not specified it is understood to begin
with 1.
n = 1, n = 2, n = 3, …
Range: Gives the TERMS of the sequence as determined by a formula, an .
Example:
an = 3n2 +1
n = 1, 2, 3, 4, 5
an = 4, 13, 28, 49, 76
Find the first 4 terms of the sequence.
1.
an = 2n
2.
an = 2n +1
3.
an = 2n -1
4.
æ 1ö
an = ç ÷
è 2ø
5.
æ 1ö
an = ç - ÷
è 2ø
6.
an = n 2
n
n
Rules For Sequences:
Rules for Sequences should be FORMULAS so you can find ANY term in the sequence.
Consider the Sequence 3, 6, 9, 12, 15
What is happening each time?
General Rule : an 
Graph the sequence of numbers by graphing the
general rule.
Domain
(which
term?)
n=1
n=2
n=3
n=4
n=5
Range
(value of
the term)
a1 = 3
a2 = 6
a3 = 9
a4 = 12
a5 = 15
Find the 100th term of the sequence:___________
Writing Rules for your sequences.
For each of the below sequences write a general rule for the nth term of the sequence.
1.)
2, 4, 6, 8,...
2.)
2 2 2
2
, ,
,
,...
5 25 125 625
n:
n:
an :
an :
General Rule: an =
General Rule: an =
3 4 5 6
, , , ...
2 3 6 7
1 1 1 1
3.)  , , , ,...
3 9 27 81
4.)
n:
n:
an :
an :
General Rule: an =
General Rule: an =
Graphing Sequences
Use your graphing calculator to create graphs of sequences.
MODE SEQ DOT ENTER
Y= Let nMin = 1
Enter the general rule as u(n)
Set a reasonable window
GRAPH
Create the graph of the sequences listed below.
1.
an = n 2
1, 4, 9, 16, 25
2.
Homework: p. 655 (9-15 odd, 21-29, 30,32,34,35)
an = (-1)n+1 (n)
1, -2, 3, -4, 5, -6