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Any such ordered arrangement of a set of numbers is called a _____
Sequence
Each of the numbers of a sequence is called a ______ of a sequence.
term
A ________ is a function whose domain is the set positive integers. It is also an ordered list of numbers.
Finite Sequence
Sequences are separated into two groups:
Infinite Sequence and Finite Sequence
Infinite Sequence
contains an infinite number of terms.
A sequence is ______ if its domain is the set of positive integers without a last term.
infinite
{1, 2, 3, 4, 5, . . . } is an example of?
Infinite sequence
(-2, -3, -4, -5, ...) is an example of?
Infinite Sequence
Finite Sequence
contains a finite number of terms.
A sequence is ______ if its domain is the set of positive integers with a last term.
finite
{1, 2, 3, 4, 5, . . . , n} is an example of?
Finite sequence
(9, 18, 27, 36, 45) is an example of?
Finite sequence
A _____ is a set of numbers written in a specific order: a_1, a_2, a_3, a_4, ...., a_n
sequence
Arithmetic sequence
is a sequence where every term after the first is obtained by adding a constant called the common difference.
Arithmetic sequence is a sequence where every term after the first is obtained by adding a constant called the ________.
Common difference
Arithmetic sequence is also called _____
Arithmetic progression
A rule that tells how to find a term using previous term is called a ______ of a sequence.
recursive definition
A sequence in which a constant d is added to the previous term to get the next term is called an __________.
Arithmetic sequence
The constant is called the _____.
common difference
2, 5, 8, 11, ... what is the common difference?
3
17, 12, 7, 2, 3, ... what is the common difference?
-5
______ is a sequence where every term after the first is obtained by adding a constant called the common difference.
Arithmetic sequence
The nth term of an arithmetic sequence with the first term a_1 and common difference d is given by:
a_n = a_1 + (n-1) d
The terms between any two nonconsecutive terms of an Arithmetic sequence are known as ________.
Arithmetic means
In an Arithmetic sequence, all the terms between any two terms are called the ______ of these two terms.
Arithmetic means
The sum of n terms of an Arithmetic sequence if the a_n (last term) is given
s_n = n/2 (a_1 +a_n)
s_n = n/2 [2a_1 + (n-1) d]
The sum of n terms of an Arithmetic sequence if a_n (last term) is not given
Sequences in which a certain number is multiplied to each term to get the next term, theses sequences are called __________.
Geometric sequences
A sequence is geometric if there exists a number r, called the ______.
Common ratio
The common ratio r can be obtained by _______ any term in the sequence by the term that precedes it.
Dividing
A Geometric sequence is a sequence where each term after the first is obtained by multiplying the preceding term by a nonzero constant called ______.
Common ratio
In an arithmetic sequence, the new term is obtained by _____ or _________ a fixed value to/from the preceding term.
adding or subtracting
Geometric sequence, wherein the new term is found by ______ or _______ a fixed value from the previous term.
multiplying or dividing
In an arithmetic sequence, the variation in the members of the sequence is ______.
linear
The variation in the elements of the _______ is exponential.
Geometric sequence
We call the terms between any two given terms of a Geometric sequence the ________.
Geometric means
An _____ is the sum of an infinite geometric sequence. This series would have no last term.
Infinite geometric series
_________ is an infinite series for which the sequence of partial sums converges.
Convergent Series
Note 
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