问题 填空题
等差数列{an}中,Sn是其前n项和,a1=-2008,
S2007
2007
-
S2005
2005
=2,则S2008
=______.
答案

∵在等差数列中S2n-1=(2n-1)an

S2007
2007
=a1004
S2005
2005
=a1003

又∵

S2007
2007
-
S2005
2005
=2

∴d=2,又由a1=-2008

Sn=a1n+

n(n-1)
2
d=n2-n-2008n,

∴S2008=-2008

故答案为:-2008

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