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satellite73 Group Title

the sequence is 2, 10, 30, 68,130, ... third differences is 6 so it is cubic what is the formula for each term?

  • one year ago
  • one year ago

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  1. satellite73 Group Title
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    i got the answer from my eyeballs, but the question is: what is the method for deriving the sequence?

    • one year ago
  2. vikrantg4 Group Title
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    what's the pattern in this sequence :/

    • one year ago
  3. experimentX Group Title
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    man ... are you trying to guess by looking? did you check my last answer ... my second last drawing!!

    • one year ago
  4. Zarkon Group Title
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    \[n^3+n\]

    • one year ago
  5. vikrantg4 Group Title
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    @satellite73 please tell what you got from your eyeballs

    • one year ago
  6. satellite73 Group Title
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    sequence is \(k^3+k\) and yes, i guessed it, it wasn't hard you know it is cubic \[2=1^3+1\]\[10=2^3+2\]\[30=3^3+3\] pattern is clear, i just wanted a snap method for getting it

    • one year ago
  7. bhaskarbabu Group Title
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    npower3+n

    • one year ago
  8. Zarkon Group Title
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    I used regression

    • one year ago
  9. satellite73 Group Title
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    @Zarkon expand...

    • one year ago
  10. satellite73 Group Title
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    please

    • one year ago
  11. Zarkon Group Title
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    I found the cubic regression formula for the above 'data' set

    • one year ago
  12. Zarkon Group Title
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    it is \[\hat{y}=x^3+x\]

    • one year ago
  13. satellite73 Group Title
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    hmmm you mean a system of equations?

    • one year ago
  14. Zarkon Group Title
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    A polynomial of degree 4 can fit in the above data...do a 'linear' regression with \[y=ax^4+bx^3+cx^2+dx+e\] you will get \[a=0,b=1,c=0,d=1,e=0\]

    • one year ago
  15. Zarkon Group Title
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    let \[x=\{1,2,3,4,5\}\] and \[y=\{2, 10, 30, 68,130\}\]

    • one year ago
  16. satellite73 Group Title
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    ok thanks. i think in this case maybe it was easier to guess, but in general not

    • one year ago
  17. Zarkon Group Title
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    sure

    • one year ago
  18. satellite73 Group Title
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    oh, but i know it is a polynomial of degree 3, because the third differences are constant. i can ignore the last term then? and use \(x=\{1,2,3,4\}\) \(y=\{2,10,30,68\}\)

    • one year ago
  19. Zarkon Group Title
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    sure

    • one year ago
  20. satellite73 Group Title
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    thnx

    • one year ago
  21. Zarkon Group Title
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    NP

    • one year ago
  22. experimentX Group Title
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    Here is another one \[ 2 + \sum_{i = 1}^{n-1}\left( 8 + \sum_{j=1}^{i-1} 12 + (j-1)6\right)\] Mathematica code .. 2 + Sum[8 + Sum[12 + (i - 1) 6, {i, 1, j - 1}], {j, 1, n - 1}] though W|A doesn't like it

    • one year ago
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