General form of a sequence of rational numbers
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What is the minimum number of terms that need to be provided to define the general term of a pattern based sequence, for example: $$1/9, 7/17,17/25$$ and so on?
sequences-and-series
asked Nov 17 at 18:03
Maan
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up vote
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favorite
What is the minimum number of terms that need to be provided to define the general term of a pattern based sequence, for example: $$1/9, 7/17,17/25$$ and so on?
sequences-and-series
asked Nov 17 at 18:03
Maan
1
1
This is not clear. "pattern based" can mean just about anything.
– lulu
Nov 17 at 18:04
1
You can never define a pattern by listing terms. In your sequence of three terms the pattern is not defined. Even if a pattern is "clear" it is no defined. The following is not a definition: $frac 12, frac 13, frac 14, frac 15, frac 16, frac 17,.....$
– fleablood
Nov 17 at 18:08
Any finite list of numbers can be fit with a polynomial.
– herb steinberg
Nov 17 at 18:10
By the way.... I have utterly no idea what the next term in your sequence is supposed to be or what "and so on" is supposed to mean. I have no idea how you went from 1/9 to 7/17 nor from 7/17 to 17/25. But even if it was crystal clear to me it wouldn't matter. It's not a definition and it wouldn't be a definition if you gave me a million terms.
– fleablood
Nov 17 at 18:11
To play with herb steinberg's comment. The next term in $frac 12, frac 13, frac 14, frac 15, frac 15, frac 17...$ is $-59$ because these terms are the solutions to $(x-frac 12)(x-frac 13)(x-frac 14)(x-frac 15)(x-frac 16)(x-frac 17)(x^2+119x + 3540) = 0$ in descending order... so... listing terms is never a definition because you can always come up with a reason the next term could be anything.
– fleablood
Nov 17 at 18:19
|
show 1 more comment
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
What is the minimum number of terms that need to be provided to define the general term of a pattern based sequence, for example: $$1/9, 7/17,17/25$$ and so on?
sequences-and-series
asked Nov 17 at 18:03
Maan
1
What is the minimum number of terms that need to be provided to define the general term of a pattern based sequence, for example: $$1/9, 7/17,17/25$$ and so on?
sequences-and-series
sequences-and-series
asked Nov 17 at 18:03
Maan
1
asked Nov 17 at 18:03
Maan
1
asked Nov 17 at 18:03
Maan
1
asked Nov 17 at 18:03
Maan
1
asked Nov 17 at 18:03
Maan
1
1
1
This is not clear. "pattern based" can mean just about anything.
– lulu
Nov 17 at 18:04
1
You can never define a pattern by listing terms. In your sequence of three terms the pattern is not defined. Even if a pattern is "clear" it is no defined. The following is not a definition: $frac 12, frac 13, frac 14, frac 15, frac 16, frac 17,.....$
– fleablood
Nov 17 at 18:08
Any finite list of numbers can be fit with a polynomial.
– herb steinberg
Nov 17 at 18:10
By the way.... I have utterly no idea what the next term in your sequence is supposed to be or what "and so on" is supposed to mean. I have no idea how you went from 1/9 to 7/17 nor from 7/17 to 17/25. But even if it was crystal clear to me it wouldn't matter. It's not a definition and it wouldn't be a definition if you gave me a million terms.
– fleablood
Nov 17 at 18:11
To play with herb steinberg's comment. The next term in $frac 12, frac 13, frac 14, frac 15, frac 15, frac 17...$ is $-59$ because these terms are the solutions to $(x-frac 12)(x-frac 13)(x-frac 14)(x-frac 15)(x-frac 16)(x-frac 17)(x^2+119x + 3540) = 0$ in descending order... so... listing terms is never a definition because you can always come up with a reason the next term could be anything.
– fleablood
Nov 17 at 18:19
|
show 1 more comment
1
This is not clear. "pattern based" can mean just about anything.
– lulu
Nov 17 at 18:04
1
You can never define a pattern by listing terms. In your sequence of three terms the pattern is not defined. Even if a pattern is "clear" it is no defined. The following is not a definition: $frac 12, frac 13, frac 14, frac 15, frac 16, frac 17,.....$
– fleablood
Nov 17 at 18:08
Any finite list of numbers can be fit with a polynomial.
– herb steinberg
Nov 17 at 18:10
By the way.... I have utterly no idea what the next term in your sequence is supposed to be or what "and so on" is supposed to mean. I have no idea how you went from 1/9 to 7/17 nor from 7/17 to 17/25. But even if it was crystal clear to me it wouldn't matter. It's not a definition and it wouldn't be a definition if you gave me a million terms.
– fleablood
Nov 17 at 18:11
To play with herb steinberg's comment. The next term in $frac 12, frac 13, frac 14, frac 15, frac 15, frac 17...$ is $-59$ because these terms are the solutions to $(x-frac 12)(x-frac 13)(x-frac 14)(x-frac 15)(x-frac 16)(x-frac 17)(x^2+119x + 3540) = 0$ in descending order... so... listing terms is never a definition because you can always come up with a reason the next term could be anything.
– fleablood
Nov 17 at 18:19
1
1
This is not clear. "pattern based" can mean just about anything.
– lulu
Nov 17 at 18:04
This is not clear. "pattern based" can mean just about anything.
– lulu
Nov 17 at 18:04
1
1
You can never define a pattern by listing terms. In your sequence of three terms the pattern is not defined. Even if a pattern is "clear" it is no defined. The following is not a definition: $frac 12, frac 13, frac 14, frac 15, frac 16, frac 17,.....$
– fleablood
Nov 17 at 18:08
You can never define a pattern by listing terms. In your sequence of three terms the pattern is not defined. Even if a pattern is "clear" it is no defined. The following is not a definition: $frac 12, frac 13, frac 14, frac 15, frac 16, frac 17,.....$
– fleablood
Nov 17 at 18:08
Any finite list of numbers can be fit with a polynomial.
– herb steinberg
Nov 17 at 18:10
Any finite list of numbers can be fit with a polynomial.
– herb steinberg
Nov 17 at 18:10
By the way.... I have utterly no idea what the next term in your sequence is supposed to be or what "and so on" is supposed to mean. I have no idea how you went from 1/9 to 7/17 nor from 7/17 to 17/25. But even if it was crystal clear to me it wouldn't matter. It's not a definition and it wouldn't be a definition if you gave me a million terms.
– fleablood
Nov 17 at 18:11
By the way.... I have utterly no idea what the next term in your sequence is supposed to be or what "and so on" is supposed to mean. I have no idea how you went from 1/9 to 7/17 nor from 7/17 to 17/25. But even if it was crystal clear to me it wouldn't matter. It's not a definition and it wouldn't be a definition if you gave me a million terms.
– fleablood
Nov 17 at 18:11
To play with herb steinberg's comment. The next term in $frac 12, frac 13, frac 14, frac 15, frac 15, frac 17...$ is $-59$ because these terms are the solutions to $(x-frac 12)(x-frac 13)(x-frac 14)(x-frac 15)(x-frac 16)(x-frac 17)(x^2+119x + 3540) = 0$ in descending order... so... listing terms is never a definition because you can always come up with a reason the next term could be anything.
– fleablood
Nov 17 at 18:19
To play with herb steinberg's comment. The next term in $frac 12, frac 13, frac 14, frac 15, frac 15, frac 17...$ is $-59$ because these terms are the solutions to $(x-frac 12)(x-frac 13)(x-frac 14)(x-frac 15)(x-frac 16)(x-frac 17)(x^2+119x + 3540) = 0$ in descending order... so... listing terms is never a definition because you can always come up with a reason the next term could be anything.
– fleablood
Nov 17 at 18:19
|
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1
This is not clear. "pattern based" can mean just about anything.
– lulu
Nov 17 at 18:04
1
You can never define a pattern by listing terms. In your sequence of three terms the pattern is not defined. Even if a pattern is "clear" it is no defined. The following is not a definition: $frac 12, frac 13, frac 14, frac 15, frac 16, frac 17,.....$
– fleablood
Nov 17 at 18:08
Any finite list of numbers can be fit with a polynomial.
– herb steinberg
Nov 17 at 18:10
By the way.... I have utterly no idea what the next term in your sequence is supposed to be or what "and so on" is supposed to mean. I have no idea how you went from 1/9 to 7/17 nor from 7/17 to 17/25. But even if it was crystal clear to me it wouldn't matter. It's not a definition and it wouldn't be a definition if you gave me a million terms.
– fleablood
Nov 17 at 18:11
To play with herb steinberg's comment. The next term in $frac 12, frac 13, frac 14, frac 15, frac 15, frac 17...$ is $-59$ because these terms are the solutions to $(x-frac 12)(x-frac 13)(x-frac 14)(x-frac 15)(x-frac 16)(x-frac 17)(x^2+119x + 3540) = 0$ in descending order... so... listing terms is never a definition because you can always come up with a reason the next term could be anything.
– fleablood
Nov 17 at 18:19