等差数列{an}的前n项和为Sn,已知a1=-2010,S20092009-S20072007=2,则S2010=().A.-2008B.2008C.-2010D.2010-数学

题目简介

等差数列{an}的前n项和为Sn,已知a1=-2010,S20092009-S20072007=2,则S2010=().A.-2008B.2008C.-2010D.2010-数学

题目详情

等差数列{an}的前n项和为Sn,已知a1=-2010,
S2009
2009
-
S2007
2007
=2,则S2010=(  ).
A.-2008B.2008C.-2010D.2010
题型:单选题难度:中档来源:不详

答案

设等差数列{an}的公差为d,则Sn=na1+
n(n-1)d
2
,即
Sn
n
=a1+
(n-1)d
2

所以
S2009
2009
-
S2007
2007
=(a1+
(2009-1)d
2
)-(a1+
(2007-1)d
2
)=d=2
又a1=-2010,,则
S2010
2010
=a1+
(2010-1)d
2
=-1,
所以S2010=-2010,
故选C.

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