问题 选择题
等差数列{an}中,Sn是其前n项和,a1=-2009,
S2007
2007
-
S2005
2005
=2
,则S2009的值为(  )
A.0B.2009C.-2009D.-2009×2009
答案

∵Sn是其前n项和,

S2007
2007
-
S2005
2005
=2,

a1+a2007
2
-
a1+a2005
2
=2

∴a2007-a2005=4,

∴d=2

∵a1=-2009,

s2009=2009×(-2009)+

2009×2008
2
×2

=2009

=-2009

故选C.

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