设Sn为等差数列{an}的前n项和,且a1=-2010,S20112011-S20082008=3,则S2011=______.-数学

题目简介

设Sn为等差数列{an}的前n项和,且a1=-2010,S20112011-S20082008=3,则S2011=______.-数学

题目详情

设Sn为等差数列{an}的前n项和,且a1=-2010,
S2011
2011
-
S2008
2008
=3
,则S2011=______.
题型:填空题难度:中档来源:不详

答案

因为数列{an}是等差数列,设其公差为d,
Sn=
n(a1+an)
2
,得:
Sn
n
=
a1+an
2

所以,
S2011
2011
-
S2008
2008
=
a1+a2011
2
-
a1+a2008
2
=
a2011-a2008
2
=class="stub"3d
2

因为
S2011
2011
-
S2008
2008
=3
,所以class="stub"3d
2
=3
,则d=2.
又a1=-2010,
所以,S2011=2011a1+
2011×(2011-1)d
2

=2011×(-2010)+class="stub"2011×2010×2
2
=0

故答案为0.

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