Find the Value of $a_{2008}$ in the Sequence

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Discussion Overview

The discussion revolves around determining the value of $a_{2008}$ in a specific sequence. Participants are analyzing the sequence's structure and attempting to identify patterns or rules that govern its progression. The inquiry appears to be conceptual and exploratory in nature.

Discussion Character

  • Exploratory
  • Debate/contested

Main Points Raised

  • Some participants present the sequence as $0,1,-1,2,3,-2,4,5,6,-3,7,8,9,10,-4,11,12,13,14,15,16,-5,--------$ and seek to find $a_{2008}$.
  • One participant questions the inclusion of the number 16 in the sequence, suggesting that its absence would simplify the problem.
  • Another participant asserts confidence in the presence of 16, indicating that its existence is critical to the complexity of the question.
  • Hints are provided by participants, but the specifics of these hints are not detailed in the posts.

Areas of Agreement / Disagreement

There is disagreement regarding the presence of the number 16 in the sequence, with some participants affirming its inclusion while others express skepticism. The overall discussion remains unresolved as participants continue to explore the implications of this uncertainty.

Contextual Notes

The discussion does not clarify the underlying rules or patterns of the sequence, leaving assumptions about its structure and the implications for calculating $a_{2008}$ unaddressed.

Albert1
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A sequence as follows :
$0,1,-1,2,3,-2,4,5,6,-3,7,8,9,10,-4,11,12,13,14,15,16,-5,--------$
please find :$a_{2008}=?$
 
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Albert said:
A sequence as follows :
$0,1,-1,2,3,-2,4,5,6,-3,7,8,9,10,-4,11,12,13,14,15,16,-5,--------$
please find :$a_{2008}=?$

are you sure that 16 is there
 
kaliprasad said:
are you sure that 16 is there
I am sure that 16 is there .
if 16 is not there , then this question will be much easier
 
Albert said:
A sequence as follows :
$0,1,-1,2,3,-2,4,5,6,-3,7,8,9,10,-4,11,12,13,14,15,16,-5,---------$
please find :$a_{2008}=?$
hint:
we have 1 number after 0
2 numbers after -1(2-3)
3 numbers after -2(4-6)
4 numbers after -3(7-10)
6 numbers after -4(11-16)
and it should have 9 numbers after -5(17-25)
can you figure out the regular pattern?
more hint:
$a_n+a_{n+2}=a_{n+3} \forall n\geq 1$
here we set $a_1=1,a_2=2,a_3=3, a_4=4,a_5=6...$
 
Last edited:
Albert said:
A sequence as follows :
$0,1,-1,2,3,-2,4,5,6,-3,7,8,9,10,-4,11,12,13,14,15,16,-5,--------$
please find :$a_{2008}=?$
[TABLE="width: 270"]
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[TD="width: 72, bgcolor: transparent"][FONT=&#26032]　
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[TD="width: 72, bgcolor: transparent"][FONT=&#26032]　
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[TD="width: 72, bgcolor: transparent"][FONT=&#26032]n
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[TD="width: 72, bgcolor: transparent"][FONT=&#26032]an
[/TD]
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[TR]
[TD="bgcolor: transparent"][FONT=&#26032]0
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]1
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]1
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]2
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]1
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-1
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]2-3
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]2
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]5
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]3
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-2
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]4-6
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]3
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]9
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]6
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-3
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]7-10
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]4
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]14
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]10
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-4
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]11-16
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]6
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]21
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]16
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-5
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]17-25
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]9
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]31
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]25
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-6
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]26-38
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]13
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]45
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]38
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-7
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]39-57
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]19
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]65
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]57
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-8
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]58-85
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]28
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]94
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]85
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-9
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]86-126
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]41
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]136
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]126
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-10
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]127-186
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]60
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]197
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]186
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-11
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]187-274
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]88
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]286
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]274
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-12
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]275-403
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]129
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]416
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]403
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-13
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]404-592
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]189
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]606
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]592
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-14
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]593-869
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]277
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]884
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]869
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-15
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]870-1275
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]406
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]1291
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]1275
[/TD]
[/TR]
[TR]
[TD="bgcolor: transparent"][FONT=&#26032]-16
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]1276-1870
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]595
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]1887
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]1870
[/TD]
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[TD="bgcolor: transparent"][FONT=&#26032]-17
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]1871-1990
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]120
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]2008
[/TD]
[TD="bgcolor: transparent"][FONT=&#26032]1990
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