Sequences and Series

1
Sequences and Series

• Use subscript notation
• Generate a sequence using a rule

2
Sequences
Finite
Infinite
2 4 3 1 4
1, 4, 7, 10
A finite sequence has a first and last term
A infinite sequence goes on forever
3
Notation
If we say an 3n - 5
a1 3(1) - 5
-2
a2 3(2) - 5
1
a3 3(3) - 5
4
a4 3(4) - 5
7
a5 3(5) - 5
10
4
Sequences
For each of the following, work out the first 6
terms, the 50th term and the 100th term. Describe
what happens as n gets larger.
rn (-2)n
an 3n 2
kn n2 2n 8
cn 7 4n
5
Converging Sequences
Which of the sequences from the previous activity
would you describe as a converging sequence and
why?
Try sketching a graph to show this.
6
Activity
Turn to page 31 of your textbook and answer
questions in exercise A.