REGULAR MATH 10 1st Quarter Reviewer

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