等差数列{an}中,Sn是其前n项和,a1=-2009,S20072007-S20052005=2,则S2009的值为()A.0B.2009C.-2009D.-2009×2009-数学

题目简介

等差数列{an}中,Sn是其前n项和,a1=-2009,S20072007-S20052005=2,则S2009的值为()A.0B.2009C.-2009D.-2009×2009-数学

题目详情

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
题型:单选题难度:中档来源:不详

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)+class="stub"2009×2008
2
×
2
=2009
=-2009
故选C.

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