There are two simple sequences – arithmetic and geometric.
An arithmetic sequence goes from one term to the next by continuously adding or subtracting the same number or value. Example: 2, 4, 6, 8, 10.. This sequence is arithmetic since it adds 2 each term. The number added or subtracted in an arithmetic sequence is called the common difference, d. In this case d=2.
A geometric sequence goes from one term to another by adding or dividing the same number or value continuously. Example: 1, 3, 9, 27.. This sequence is geometric since it multiplies 3 each term. The number multiplied or divided in a geometric sequence is called the common ratio, r. In this case r=3.
There are 3 rules of infinite limits: 1. If the power of the top is the same as the power of the bottom, take the coefficients: 4x^2 + 3x + 7/2x+2 + 2x + 1 = 4/2 = 2 2. If the power of the bottom is larger than the power of the top, the limit is zero: x^2 + 4x/x^3 + 7x = 0 3. If the power of the top is larger than the power of the bottom, the limit does not exist: x^3 + 3x -7/x^2 + 4x = does not exist
The two main types of sequences that they have in math are arithmetic and geometric. (A sequence can also be neither if it does not follow any of the specific patterns.)
An arithmetic sequence is when a number is added or subtracted to a list of numbers that goes on and on. An example of this type of sequence would be something like:
5, 10, 15, 20,… ; 5 is being added to the number each time. Or 27, 22, 17, 12, 7…. ; in this case, 5 is being subtracted each time.
A geometric sequence is when a number is multiplied or divided to a list of number that keeps going on and on. For example:
3, 12, 48, 192,…. ; 4 is being multiplied each time. Or 256, 64, 16, 4…. ; 4 is being divided each time.
To find limits, there are about 3 rules:
1. If the power of the top is the same as the bottom, you take its coefficients. 3n^4/12n^4 = 3/12 = ¼
2. If the power of the bottom is larger than the power of the top, the limit is zero. 4n^3/ n^5 = 0
3. If the power of the top is larger than the power of the bottom, the limit does not exist and it will be infinity. 5n^7/ 2n^5 = infinity
A sequence in math is simply a list of numbers. An arithmetic sequence is where the same number is added or subtracted each time. For example: 3,6,9,12 : The sequence is add 3 11,14,17,20 : The sequence is add 3
A geometric sequence is where the same number is multiplied each time. For example: 2,4,8,16 : The sequence is times 2 3,4.5,5,6.75 : The sequence is times 2/3
In math the term limit is more a target, of what to reach. To find a limit there are rules
1. If the polynomials highest exponent equals the bottoms the answer is the coefficent. n^2+17/3n^2-3n = 1/3
2. If the polynomials highest exponent is greater than the bottom the answer is +/- infinity. 7n^3/4n^2-8 = infinity
3.If the polynomials highest exponent is less the tthe bottom numbers answer is 0. 6n^3+6n/7n^4-25 = 0
*If rules do not apply you use a table and figure out what is is approaching. (.99)^n "r^n=0 iffinite absolute value r is less than 1" When plugged into the chart you get the answer .366,...,.0004...,.000002, and so on which gets you to zero
Chapter thirteen teaches everything you need to know about sequences and series. We learned in section one about the two main types of sequences: Arithmetic and geometric. In order for a sequence to be classified as an arithmetic or geometric sequence, it must follow all the rules for each. Nevertheless, if the sequence follows neither the rules for a geometric sequence nor an arithmetic sequence, it is therefore classified as neither. An arithmetic sequence is a sequence where the SAME number is being added or subtracted each time. Ex. 1, 2,3,4,5 Here the common difference, d, is 1 because 1 is being added to each number each time. Ex. 12, 6, 0, -6, -12 The d=-6 the number (-6) is being added each time which therefore makes the sequence an arithmetic one.
A geometric sequence is a sequence where the same number is being multiplied each time. Ex. 10,20,40,80 The common ratio, r (the number being multiplied), is 2. In order to determine if a sequence id geometric or arithmetic you simply look to see if the difference between the numbers are changes due to addition or subtraction (arithmetic) or multiplication and division ( geometric). The rules for limits are as follows: 1. If the highest degree at the top is equal to the highest degree at the bottom then the answer is the coefficient 2. If the degree at the top is greater than the degree at the botton the the answer is +/- infinity. 3. If the top degree is less than the highest degree of the bottom degree, the answer is zer0. :)
An arithmetic sequence is a term that has a number being added or subtracted to it to get a new term. An example of an arithmetic sequence is 4, 13, 22, 31, 40 because you add 9 to each new term to get another one.
A geometric sequence is a term that has a number being multiplied or divided to it to get a new term. An example of a geometric sequence is 4, 36, 324, 2916 because you multiply 9 to get each new to get another term.
http://www.purplemath.com/modules/series3.htm
There are three main rules for finding limits.
1 If ° top = ° bottom answer is coefficient; Example: 4n3 + 4/ 5n3 + 2
2 if ° top > ° bottom answer is +/- ∞; Example: 3n2 + 1/ 2n + 2
3 If ° top < ° bottom answer is 0; Example: 5n4/ 6n5 + 2
It's very easy to determine whether a sequence is arithmetic or geometric. an ARITHMETIC sequence is just a sequence where the same number is being added or subtracted each time. EXAMPLE: 3, 5, 7, 9, 11..... *it adds 2 each time so its arithmetic.
30, 26, 22, 18, 14.... *you are subtracting 3 each time so its arithmetic also.
***whatever is being added or subtracted each time is d (common difference)
a GEOMETRIC sequence is where the same number is being multiplied or divided each time. EXAMPLE: 32, 16, 8, 4, 2.... *2 is being divided each time so its geometric.
3, 9, 27, 81, 243..... **pay close attention! 3 is being multiplied each time!
LIMITS: there are 3 rules.
if the exponent on the top is the same as the exponent on the bottom the answer is coefficient. EXAMPLE: 3x^2+4/2x+3----since both exponents are the same your answer is 3/2
if the exponent on the top is greater than the exponent on the bottom your answer is +/- infinity. EXAMPLE: 2x^2/5x-----top exponent is larger! its postive infinity.
if the exponent at the top is less than the exponent at the bottom then your answer is 0. EXAMPLE: 9x^2-1 / 7x^4+1-------top exponent is less! your answer is 0.
I used no online sources. All of this was in our notes.
Arithmetic sequence is a sequence where the same number is added or subtracted each time. For example: 4, 10, 16, 22….; 6 is being added to the number each time. 30, 25, 20, 15….; 5 is being subtracted to the number each time.
Geometric sequence is a sequence where the same number is multiplied or divided each time. For example: 4, 16, 64, 256….; 4 is being multiplied to the number each time. 256, 64, 16, 4….; 4 is being divided to the number each time.
To find limits, there are 3 rules:
1. If the power of the top is the same as the bottom, you take its coefficients.
Example: n^2+1/2n^2-3n= ½ is the answer
2. If the power of the bottom is larger than the power of the top, the limit is zero.
Example: 5n^2+square root of n/3n^3+7=0 is the answer
3. If the power of the top is larger than the power of the bottom, the limit does not exist and it will be infinity.
A term that has a number being added or subtracted to it to get a new term would be classified as an arithmetic sequence.
An example of an arithmetic sequence is 2, 8, 14, 20, 26. This is an arithmetic sequence because you add 6 to get the next term each time.
A term that has a number being multiplied or divided to it to get a new term is classified as a geometric sequence. 8, 24, 72, 216 is an example of a geometric sequence because the term is multiplied by 3 each time.
There are to kinds of sequences that you can use and they are arithmetic and geometric.
When using an arithmetic sequence a number is either going to be added or subtracted in the sequence. When using a geometric sequence a number is either going to be multiplied or divided to the sequence.
Example of an arithmetic sequence: 10,20,30,40... you are adding ten each time.
Example of a geometric sequence: 4,8,16,32... you are multiplying two each time.
Here are the rules that are used to follow limits. rule 1: if the degree at the top is equal to the degree at the bottom the answer is the coefficient. example: 2n^3+2/5n^3 the answer is equal to 2/5.
rule 2: If the degree at the top is greater than the degree at the bottom the answer is +/- infinity. example: 9n^2/4n your answer is going to be +infinity.
rule 3: If the degree at the top is less than the degree at the bottom the answer is going to be equal to 0. example:10n^8/14n^9 your answer is going to be 0
I took of of my information and resources directly from my notes :)
There are two simple sequences – arithmetic and geometric.
ReplyDeleteAn arithmetic sequence goes from one term to the next by continuously adding or subtracting the same number or value.
Example: 2, 4, 6, 8, 10..
This sequence is arithmetic since it adds 2 each term.
The number added or subtracted in an arithmetic sequence is called the common difference, d. In this case d=2.
A geometric sequence goes from one term to another by adding or dividing the same number or value
continuously.
Example: 1, 3, 9, 27..
This sequence is geometric since it multiplies 3 each term.
The number multiplied or divided in a geometric sequence is called the common ratio, r. In this case r=3.
There are 3 rules of infinite limits:
1. If the power of the top is the same as the power of the bottom, take the coefficients:
4x^2 + 3x + 7/2x+2 + 2x + 1 = 4/2 = 2
2. If the power of the bottom is larger than the power of the top, the limit is zero:
x^2 + 4x/x^3 + 7x = 0
3. If the power of the top is larger than the power of the bottom, the limit does not exist:
x^3 + 3x -7/x^2 + 4x = does not exist
http://www.physicsforums.com/showthread.php?t=52223
http://www.purplemath.com/modules/series3.htm
The two main types of sequences that they have in math are arithmetic and geometric. (A sequence can also be neither if it does not follow any of the specific patterns.)
ReplyDeleteAn arithmetic sequence is when a number is added or subtracted to a list of numbers that goes on and on. An example of this type of sequence would be something like:
5, 10, 15, 20,… ; 5 is being added to the number each time. Or
27, 22, 17, 12, 7…. ; in this case, 5 is being subtracted each time.
A geometric sequence is when a number is multiplied or divided to a list of number that keeps going on and on. For example:
3, 12, 48, 192,…. ; 4 is being multiplied each time. Or
256, 64, 16, 4…. ; 4 is being divided each time.
To find limits, there are about 3 rules:
1. If the power of the top is the same as the bottom, you take its coefficients.
3n^4/12n^4 = 3/12 = ¼
2. If the power of the bottom is larger than the power of the top, the limit is zero.
4n^3/ n^5 = 0
3. If the power of the top is larger than the power of the bottom, the limit does not exist and it will be infinity.
5n^7/ 2n^5 = infinity
http://math.about.com/od/algebra/a/Sequences.htm
http://www.physicsforums.com/showthread.php?t=52223
A sequence in math is simply a list of numbers. An arithmetic sequence is where the same number is added or subtracted each time.
ReplyDeleteFor example:
3,6,9,12 : The sequence is add 3
11,14,17,20 : The sequence is add 3
A geometric sequence is where the same number is multiplied each time.
For example:
2,4,8,16 : The sequence is times 2
3,4.5,5,6.75 : The sequence is times 2/3
In math the term limit is more a target, of what to reach. To find a limit there are rules
1. If the polynomials highest exponent equals the bottoms the answer is the coefficent.
n^2+17/3n^2-3n = 1/3
2. If the polynomials highest exponent is greater than the bottom the answer is +/- infinity.
7n^3/4n^2-8 = infinity
3.If the polynomials highest exponent is less the tthe bottom numbers answer is 0.
6n^3+6n/7n^4-25 = 0
*If rules do not apply you use a table and figure out what is is approaching.
(.99)^n
"r^n=0 iffinite absolute value r is less than 1"
When plugged into the chart you get the answer .366,...,.0004...,.000002, and so on which gets you to zero
Chapter thirteen teaches everything you need to know about sequences and series. We learned in section one about the two main types of sequences: Arithmetic and geometric. In order for a sequence to be classified as an arithmetic or geometric sequence, it must follow all the rules for each. Nevertheless, if the sequence follows neither the rules for a geometric sequence nor an arithmetic sequence, it is therefore classified as neither.
ReplyDeleteAn arithmetic sequence is a sequence where the SAME number is being added or subtracted each time.
Ex. 1, 2,3,4,5
Here the common difference, d, is 1 because 1 is being added to each number each time.
Ex. 12, 6, 0, -6, -12
The d=-6 the number (-6) is being added each time which therefore makes the sequence an arithmetic one.
A geometric sequence is a sequence where the same number is being multiplied each time.
Ex. 10,20,40,80
The common ratio, r (the number being multiplied), is 2.
In order to determine if a sequence id geometric or arithmetic you simply look to see if the difference between the numbers are changes due to addition or subtraction (arithmetic) or multiplication and division ( geometric).
The rules for limits are as follows:
1. If the highest degree at the top is equal to the highest degree at the bottom then the answer is the coefficient
2. If the degree at the top is greater than the degree at the botton the the answer is +/- infinity.
3. If the top degree is less than the highest degree of the bottom degree, the answer is zer0.
:)
An arithmetic sequence is a term that has a number being added or subtracted to it to get a new term. An example of an arithmetic sequence is 4, 13, 22, 31, 40 because you add 9 to each new term to get another one.
ReplyDeleteA geometric sequence is a term that has a number being multiplied or divided to it to get a new term. An example of a geometric sequence is 4, 36, 324, 2916 because you multiply 9 to get each new to get another term.
http://www.purplemath.com/modules/series3.htm
There are three main rules for finding limits.
1 If ° top = ° bottom answer is coefficient; Example: 4n3 + 4/ 5n3 + 2
2 if ° top > ° bottom answer is +/- ∞; Example:
3n2 + 1/ 2n + 2
3 If ° top < ° bottom answer is 0; Example: 5n4/ 6n5 + 2
From the notes you gave us
It's very easy to determine whether a sequence is arithmetic or geometric.
ReplyDeletean ARITHMETIC sequence is just a sequence where the same number is being added or subtracted each time.
EXAMPLE:
3, 5, 7, 9, 11.....
*it adds 2 each time so its arithmetic.
30, 26, 22, 18, 14....
*you are subtracting 3 each time so its arithmetic also.
***whatever is being added or subtracted each time is d (common difference)
a GEOMETRIC sequence is where the same number is being multiplied or divided each time.
EXAMPLE:
32, 16, 8, 4, 2....
*2 is being divided each time so its geometric.
3, 9, 27, 81, 243.....
**pay close attention! 3 is being multiplied each time!
LIMITS:
there are 3 rules.
if the exponent on the top is the same as the exponent on the bottom the answer is coefficient.
EXAMPLE:
3x^2+4/2x+3----since both exponents are the same your answer is 3/2
if the exponent on the top is greater than the exponent on the bottom your answer is +/- infinity.
EXAMPLE:
2x^2/5x-----top exponent is larger! its postive infinity.
if the exponent at the top is less than the exponent at the bottom then your answer is 0.
EXAMPLE:
9x^2-1 / 7x^4+1-------top exponent is less! your answer is 0.
I used no online sources. All of this was in our notes.
arithmetic and geometric sequences:
ReplyDeleteArithmetic sequence is a sequence where the same number is added or subtracted each time. For example: 4, 10, 16, 22….; 6 is being added to the number each time.
30, 25, 20, 15….; 5 is being subtracted to the number each time.
Geometric sequence is a sequence where the same number is multiplied or divided each time. For example: 4, 16, 64, 256….; 4 is being multiplied to the number each time.
256, 64, 16, 4….; 4 is being divided to the number each time.
To find limits, there are 3 rules:
1. If the power of the top is the same as the bottom, you take its coefficients.
Example: n^2+1/2n^2-3n= ½ is the answer
2. If the power of the bottom is larger than the power of the top, the limit is zero.
Example: 5n^2+square root of n/3n^3+7=0 is the answer
3. If the power of the top is larger than the power of the bottom, the limit does not exist and it will be infinity.
Example:7n^3/4n^2-5= infinity
A term that has a number being added or subtracted to it to get a new term would be classified as an arithmetic sequence.
ReplyDeleteAn example of an arithmetic sequence is 2, 8, 14, 20, 26. This is an arithmetic sequence because you add 6 to get the next term each time.
A term that has a number being multiplied or divided to it to get a new term is classified as a geometric sequence.
8, 24, 72, 216 is an example of a geometric sequence because the term is multiplied by 3 each time.
Below are three rules mainly used to find limits:
1 If ° top = ° bottom answer is coefficient
Example: 7n^6+3/9n^6 answer is 7/9
2 if ° top > ° bottom answer is +/- ∞
Example: 7n^6/9n answer is + ∞
3 If ° top < ° bottom answer is 0
Example: 7n^6/ 9n^8 + 4 answer is 0
All information is from the notes given in class.
There are to kinds of sequences that you can use and they are arithmetic and geometric.
ReplyDeleteWhen using an arithmetic sequence a number is either going to be added or subtracted in the sequence. When using a geometric sequence a number is either going to be multiplied or divided to the sequence.
Example of an arithmetic sequence:
10,20,30,40...
you are adding ten each time.
Example of a geometric sequence:
4,8,16,32...
you are multiplying two each time.
Here are the rules that are used to follow limits.
rule 1: if the degree at the top is equal to the degree at the bottom the answer is the coefficient.
example: 2n^3+2/5n^3 the answer is equal to 2/5.
rule 2: If the degree at the top is greater than the degree at the bottom the answer is +/- infinity.
example: 9n^2/4n your answer is going to be +infinity.
rule 3: If the degree at the top is less than the degree at the bottom the answer is going to be equal to 0.
example:10n^8/14n^9 your answer is going to be 0
I took of of my information and resources directly from my notes :)