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satellite73
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the sequence is 2, 10, 30, 68,130, ...
third differences is 6 so it is cubic
what is the formula for each term?
 2 years ago
 2 years ago
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?
 2 years ago
 2 years ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.0
i got the answer from my eyeballs, but the question is: what is the method for deriving the sequence?
 2 years ago

vikrantg4 Group TitleBest ResponseYou've already chosen the best response.0
what's the pattern in this sequence :/
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
man ... are you trying to guess by looking? did you check my last answer ... my second last drawing!!
 2 years ago

vikrantg4 Group TitleBest ResponseYou've already chosen the best response.0
@satellite73 please tell what you got from your eyeballs
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
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
 2 years ago

bhaskarbabu Group TitleBest ResponseYou've already chosen the best response.0
npower3+n
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.3
I used regression
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
@Zarkon expand...
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.3
I found the cubic regression formula for the above 'data' set
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.3
it is \[\hat{y}=x^3+x\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
hmmm you mean a system of equations?
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.3
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 \[a=0,b=1,c=0,d=1,e=0\]
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.3
let \[x=\{1,2,3,4,5\}\] and \[y=\{2, 10, 30, 68,130\}\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
ok thanks. i think in this case maybe it was easier to guess, but in general not
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
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 \(x=\{1,2,3,4\}\) \(y=\{2,10,30,68\}\)
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
Here is another one \[ 2 + \sum_{i = 1}^{n1}\left( 8 + \sum_{j=1}^{i1} 12 + (j1)6\right)\] Mathematica code .. 2 + Sum[8 + Sum[12 + (i  1) 6, {i, 1, j  1}], {j, 1, n  1}] though WA doesn't like it
 2 years ago
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