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Question
Sorry I am asking you another question, its just your the only one who could do this math....
A sequence {asubn} is defined recursively by asub1=1, asub2=4, asub3=9 and asubn=asub(n-1)-asub(n-2)+asub(n-3)+
2(2n-3) for n >or equal to 4.
a.) Conjecture a formula for asubn
b.) Prove that your conjecture is correct.
I just don't get it... :(
The frist 3 terms are given
1, 4, and 9.
Each term after that is defined as term(n-1)-term(n-2)+term(n-3).
This means that the next term would be 9-4+1=6.
The terms we have found our now 1,4,9 and 6.
The next term is 6-9+4=1.
The terms we have found are 1,4,9,6 and 1.
The next term is 1-6+9=4.
The terms we have found are 1,4,9,6,1, and 4.
It's starting to look repetetive.
The next term is 4-1+6=9.
The terms we have found are 1,4,9,6,1,4 and 9.
It's almost repetitive for sure.
The next term is 9-4+1=6.
The terms so far are now 1,4,9,6,1,4,9, and 6.
After looking at the results, the next term was done four iterations ago and the formula is -(((5x-33)x+55)x-30)/3 if we take
x as n mod 4.
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Scott A Wilson
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