Find all pairs of numbers, which meet the assumption.
I have to find all pairs of numbers $ c, d in mathbb{R}^2 $, which meet the assumption.
The assumption is:
$ S_n = (c-5d)n^2+ncd^2-2c^2-2d^2+c+d $
is the sum of the first n words of some arithmetic sequence.
So I wrote a formula for the sum of the first n words of arithmetic sequence;
$ S_n= {2a_1n+n^2r-rnover 2} $
Where $n$ is the number of numbers of the arithmetical sequence, $r$ is difference and $a_1$ is the first number.
So now I have:
$2(c-5d)=r $
$2cd^2=2a_1-r$
What should do now? I do not want to insert a number as $r$ or $a_1$ or even $n$.
Thanks in advice
sequences-and-series systems-of-equations arithmetic square-numbers
asked Dec 2 '18 at 13:12
Kukoz
207
add a comment |
I have to find all pairs of numbers $ c, d in mathbb{R}^2 $, which meet the assumption.
The assumption is:
$ S_n = (c-5d)n^2+ncd^2-2c^2-2d^2+c+d $
is the sum of the first n words of some arithmetic sequence.
So I wrote a formula for the sum of the first n words of arithmetic sequence;
$ S_n= {2a_1n+n^2r-rnover 2} $
Where $n$ is the number of numbers of the arithmetical sequence, $r$ is difference and $a_1$ is the first number.
So now I have:
$2(c-5d)=r $
$2cd^2=2a_1-r$
What should do now? I do not want to insert a number as $r$ or $a_1$ or even $n$.
Thanks in advice
sequences-and-series systems-of-equations arithmetic square-numbers
asked Dec 2 '18 at 13:12
Kukoz
207
add a comment |
I have to find all pairs of numbers $ c, d in mathbb{R}^2 $, which meet the assumption.
The assumption is:
$ S_n = (c-5d)n^2+ncd^2-2c^2-2d^2+c+d $
is the sum of the first n words of some arithmetic sequence.
So I wrote a formula for the sum of the first n words of arithmetic sequence;
$ S_n= {2a_1n+n^2r-rnover 2} $
Where $n$ is the number of numbers of the arithmetical sequence, $r$ is difference and $a_1$ is the first number.
So now I have:
$2(c-5d)=r $
$2cd^2=2a_1-r$
What should do now? I do not want to insert a number as $r$ or $a_1$ or even $n$.
Thanks in advice
sequences-and-series systems-of-equations arithmetic square-numbers
asked Dec 2 '18 at 13:12
Kukoz
207
I have to find all pairs of numbers $ c, d in mathbb{R}^2 $, which meet the assumption.
The assumption is:
$ S_n = (c-5d)n^2+ncd^2-2c^2-2d^2+c+d $
is the sum of the first n words of some arithmetic sequence.
So I wrote a formula for the sum of the first n words of arithmetic sequence;
$ S_n= {2a_1n+n^2r-rnover 2} $
Where $n$ is the number of numbers of the arithmetical sequence, $r$ is difference and $a_1$ is the first number.
So now I have:
$2(c-5d)=r $
$2cd^2=2a_1-r$
What should do now? I do not want to insert a number as $r$ or $a_1$ or even $n$.
Thanks in advice
sequences-and-series systems-of-equations arithmetic square-numbers
sequences-and-series systems-of-equations arithmetic square-numbers
asked Dec 2 '18 at 13:12
Kukoz
207
asked Dec 2 '18 at 13:12
Kukoz
207
edited Dec 5 '18 at 22:01
asked Dec 2 '18 at 13:12
Kukoz
207
asked Dec 2 '18 at 13:12
Kukoz
207
asked Dec 2 '18 at 13:12
Kukoz
207
207
add a comment |
add a comment |
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