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

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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]　
[/TD]
[TD="width: 72, bgcolor: transparent"][FONT=&#26032]　
[/TD]
[TD="width: 72, bgcolor: transparent"][FONT=&#26032]n
[/TD]
[TD="width: 72, bgcolor: transparent"][FONT=&#26032]an
[/TD]
[/TR]
[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]
[/TR]
[TR]
[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
[/TD]
[/TR]
[/TABLE]
 

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