4.1 - 4.2

Sequence

A special type of function in which the domain is a set of consecutive integers

How would you denote the input of a sequence?

Fvn, ex. Fv0 = 0

A value Fvk is called a ___ of the sequence of k is the ___ of Fvk

term, index

How do you denote the entire sequence versus a single term?

{Fvk} vs. Fvk

A sequence {avk} with a finite domain {m,…,n} is a ____ ____

the __ is m, and avm is the _

the __ __ final index is n, and avn _ _

finite sequence

initial index, initial term

final index, final term

A sequence with an infinite domain is an ___ ___

there is an initial index and initial term, but no __ ___ or __ __

infinite sequence

final index, final term

explicit formula

shows how the value of term avk depends onk.

A sequence is increasing if for every two consecutive indices k and k+1 in the domain

a v k < a v k+1

A sequence is non-decreasing if for every two consecutive indices k and k+1 in the domain

avk <= av k+1

A sequence is decreasing if for every two consecutive indices k and k+1 in the domain

avk > av k+1

A sequence is non-increasing if for every two consecutive indices k and k+1 in the domain

avk >= av k+1

arithmetic sequence

a sequence of real numbesr in which the difference between any two consecutive terms is a constant, called the difference

ex. 2,5,8,11,… d = 3

geometric sequence

a sequence of real numbers in which the ratio between any two conseuctive terms is a constant, call the common ratio

ex. 3,6,12,24,48,.. r =2

true or false: sequences have to be arithmetic or geometric

false