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Source: College Mathematics
, Rockswold G., Bennett J., and Briggs W.
C:/CLASES_COLEGIO/2007/NOTAS/0102/
02//07
Math 1332  College Mathematics
Chapter 81 & 82 Notes
Sequences and Series
Sequences
A sequence is a function that computes an ordered list.
Infinite sequence
is a function that has the set of natural numbers as its domain (
D = {1, 2, 3, …}
.
Finite sequence
is a function with domain
D = {1, 2, 3, …, n}
, for some fixed natural number
n
.
Let us consider the examples we previously learned when comparing linear growth versus
exponential growth to understand what sequences are and what types there are:
Note
Æ
with respect to the definition of a sequence, our domain is restricted to natural numbers!
f(n) = 2n
f(n) = 2
n
What is the pattern, common difference or ratio in your output values?
2, 4, 6, 8
2, 4, 8, 16
l
l
l
l
▼
▼
d
(difference) =
r
(ratio) =
If there exists a Common Difference
d
that we add to the previous term (in output), then we deal
with what is called an Arithmetic Sequence
.
In the example, we have a linear function.
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This note was uploaded on 01/05/2012 for the course MATH 1332.S0 taught by Professor Mariselaa.martinez during the Fall '11 term at Collin College.
 Fall '11
 MariselaA.Martinez
 Natural Numbers, Sequences And Series

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