Examples: "3,6,7,9" "4,3,2,1"

Series: The sum of an infinite sequence.

Ex: "a,b,c = a+b+c"

"f,v,z = f+v+z"

Math is Fun (2015) "Sequences" Retrieved from:

http://www.mathsisfun.com/algebra/sequences-series.html

Ex: 3,5,7,9..

Ex: 5,10,15,20...

If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an arithmetic sequence.

Ex: 2, 5, 8, 11, 14,...

Ex: 7, 3, –1, –5,... 

If a sequence of values follows a pattern of multiplying a fixed amount (not zero) times each term to arrive at the following term, it is referred to as a geometric sequence.

 Ex: 1, 2, 4, 8, 16,... 

 Ex: 81, 27, 9, 3, 1, 1/3,...

Serie: is informally the result of adding all those terms together: a₁ + a₂ + a₃ + . These can be written more compactly using the summation symbol ∑.

Ex: 2 – 4 + 6 – 8 + 10

Ex: 1 + 1 + 3 + 7 + 17 + 41 = 70

Bibliography:

http://www.purplemath.com/modules/series3.htm

Video:

https://www.youtube.com/watch?v=L2PTZFbkJVg

Series: The sum of the terms in a sequence.

https://m.youtube.com/watch?v=WdCQV44QtpU

The sum of the terms of a sequence is called a series. While some sequences are simply random values, other sequences have a definite pattern that is used to arrive at the sequence's terms. Two such sequences are the arithmetic and geometric sequences.

Examples:

1)20, 25, 30, 35, ...

2) f, r, e, d...

Evaluating sequences:

is to take a look at a pattern, by next having to take what value its between each number, and having to take what sequence its between each one

Examples:

1) 2(0) + 2(1) + 2(2) +2(3) + 2(4) =

2) a1 + a2 + a3 + a4 + a5 =

Arithmetic  sequences and series

If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an  arithmetic sequence.  The number added to each term is constant (always the same).

Examples:

1) 1, 4, 7, 10, 13, 16, ...

2) 15, 10, 5, 0, -5, -10, ...

Geometric Sequences and series

A sequence is an ordered list of numbers. The sum of the terms of a sequence is called a series. While some sequences are simply random values, other sequences have a definite pattern that is used to arrive at the sequence's terms. Two such sequences are the arithmetic and geometric sequences.

Examples:

1) 5, 10, 20, 40, ...

2) -11, 22, -44, 88, ...

Video Link:

https://www.youtube.com/watch?v=oRMW_LfuaT4

Bibliography:

1)http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm

2)http://www.regentsprep.org/regents/math/algtrig/atp2/geoseq.htm

3) http://www.purplemath.com/modules/series2.htm

A "sequence" is an ordered list of numbers; the numbers in this ordered list are called "elements" or "terms". A "series" is the value you get when you add up all the terms of a sequence; this value is called the "sum". 

Sequence: 7, 8, 9, 10...

Series: 7+8+9+10=34

-A Sequence is a list of things (usually numbers) that are in order.

ex. 1,2,3

ex2. 4-3-2-1

What is a serie?

-Value obtained with the sum of all numbers in a sequence.

ex. 77, 78, 79 ; becomes 77+78+79

How do you evaluate a Sequence?

-In order to evaluate a sequence, you need to find the difference between each term and write it in a formula.

ex. 3 , 9 , 27 , 81 , 243...

Formula: N x 3 (N is the position in the sequence)

-In an Arithmetic Sequence the difference between one term and the other is constant.

(This sequence has a difference of 3 between each number.)

Geometric Sequence:

-In a Geometric Sequence each term is found by multiplying the previous term by a constant.

ex. 2, 4, 8, 16, 32, 64, 128, 256... (Each term (except the first term) is found by multiplying the previous term by 2.)

Geometric Series:

-In a Geometric Serie you just need to add each term in the Geometric Sequence.

ex. 

2, 4, 8, 16, 32, 64, 128, 256...

becomes

2+4+8+16+32+64+128+256...

Bibliography:

https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html

http://www.purplemath.com/modules/series.htm

The sum of the terms of a sequence is called a series. While some sequences are simply random values, other sequences have a definite pattern that is used to arrive at the sequence's terms. Two such sequences are the arithmetic and geometric sequences.

Ex: 3, 6, 9, 12

Ex: 3, 5, 7, 9

What is a serie?

A series is, informally speaking, the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely

Ex.: '1,3,5' 1+3+5

What is evaluating sequences?

A sequence of values follows a pattern of multiplying a fixed amount (not zero) times each term to arrive at the following term, it is referred to as a  geometric sequence.  The number multiplied each time is constant (Always the same)

What is a Arithmetic sequence?

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2.

What is the Geometric Sequences?

Is the fixed amount multiplied is called the common ratio, r, referring to the fact that the ratio (fraction) of the second term to the first term yields this common multiple. To find the common ratio, divide the second term by the first term

What is the geometric series?

In mathematics, a geometric series is a series with a constant ratio between successive terms

http://www.regentsprep.org/

A Sequence is a list of things (usually numbers) that are in order.

A serie is an infinite ordered set of terms combined together by the addition operator.

Examples:

{1, 2, 3, 4, ...} is a very simple sequence (and it is an infinite sequence)

{20, 25, 30, 35, ...} is also an infinite sequence

A sequence is an ordered list of numbers.   The sum of the terms of a sequence is called aseries.

4,7,10,13,16 d=3

1,-2,4,-8,16 d=x(-2)

1,2,3,4,5,6,7,8,9,10,11,12,13,14 d=1

https://www.youtube.com/watch?v=_cooC3yG_p0&feature=youtu.be

example: 3,5,7,9....

Serie: the addition of al the numbers of the sequence

example: 2,6,10,14,18 = 50

Arithmetic sequence: a sequence becomes arithmetic when the difference between numbers is constant

example: 3,7,11,15,19

{20, 25, 30, 35, ...} it is an infinite sequence

{4, 3, 2, 1} is 4 to 1 backwards

Series: A sum of an infinite sequence

Sequence: {1, 3, 5, 7, ...}

Series: 1 + 3 + 5 + 7 + …

Sequence: (5,10,15,20)

Series: 5 + 10 + 15 +20 + ….

Evaluating a sequence: A sequence of values follows a pattern of multiplying a fixed amount (not zero) times each term to arrive at the following term, it is referred to as a  geometric sequence.  The number multiplied each time is constant (Always the same).

The formula for the first n terms of an arithmeticsequence, starting with n = 1, is with the symbol: ∑

Arithmetic Sequence: In an Arithmetic Sequence the difference between one term and the next is a constant. In other words, we just add the same value each time ... infinitely.  An arithmetic series: is the sum of an arithmetic sequence

Geometric Sequence: each term is found by multiplying the previous term by a constant.

This sequence has a factor of 2 between each number.

Each term (except the first term) is found by multiplying the previous term by 2.

{a, ar, ar2, ar3, ... }

Geometric series: is the sum of a geometric sequence.

References

Pierce, Rod. (18 Sep 2014). "Sequences". Math Is Fun. Retrieved 28 Apr 2015 from http://www.mathsisfun.com/algebra/sequences-series.html

Pierce, Rod. (18 Sep 2014). "Arithmetic Sequences and Sums". Math Is Fun. Retrieved 28 Apr 2015 from http://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html

Pierce, Rod. (18 Sep 2014). "Geometric Sequences and Sums". Math Is Fun. Retrieved 28 Apr 2015 from http://www.mathsisfun.com/algebra/sequences-sums-geometric.html

Example Sequence: 3, 5, 7, 9, ... is a sequence starting at 3 and increasing by 2 each time.

Serie: is the value you get when you add up all the terms of a sequence; this value is called the "sum". For instance, "1, 2, 3, 4" is a sequence, with terms "1", "2", "3", and "4". The corresponding series is the sum "1 + 2 + 3 + 4", and the value of the series is 10.

Example Serie: a₁ + a₂ + a₃ + a₄ + a₅ = 1 + 3 + 5 + 7 + 9 = 25

Sequence Video:

https://www.youtube.com/watch?v=Kxh7yJC9Jr0

Series Video:

https://www.youtube.com/watch?v=7EoUccjjD-c

Bibliography:

www.mathisfun.com (2014). Sequences. [Web log post] http://www.mathsisfun.com/algebra/sequences-series.html

Stapel, E. (2015). Sequences and Series. [Web log post] http://www.purplemath.com/modules/series.htm