CalcBC
Chp 111
Sequences
Notes
1.
SEQUENCE
–
An ordered list of numbers
"Ordered" means the numbers are not randomly listed, instead they came from a
formula/expression where consecutive positive integers were used to create a list
TERMS
–
The numbers in a sequence
typically terms are denoted as
a
1
,
a
2
,
a
3
,
a
4
,
… ,
a
n
where the subscripts indicate the place in the sequence
a
n
Is the
"
nth term
"
It is the
GENERAL TERM
It is also referenced as the
last term of a FINITE sequence
,
or the
term approaching the faaaaaaaaarrrrrrrrrrrr end of an infinite sequence
GENERAL TERM

The formula/expression used to make a sequence
(used to define the sequence)
Ex
a
n
=
a
n
=
a
n
= 3n + 1
* Where
n
can be
0
and
positive integers only
Ex(figure out the explicit general term)
—
Given each sequence find the general term a
n
.
(a)
(b)
2.
CONVERGE

Sequence approaches a specific value
(it does not go to infinity)
Theorem:
A sequence converges if
=
L ,
otherwise it diverges
Ex(graphical look at a sequence)
—
For each sequence determine if the sequence converges or diverges.
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 Spring '10
 KNOPF
 Integers, Natural number

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