等差数列{an}中,Sn是前n项和,a1=-2010,S20072007-S20052005=2,则S2013的值为______.-数学

题目简介

等差数列{an}中,Sn是前n项和,a1=-2010,S20072007-S20052005=2,则S2013的值为______.-数学

题目详情

等差数列{an}中,Sn是前n项和,a1=-2010,
S2007
2007
-
S2005
2005
=2
,则S2013的值为______.
题型:填空题难度:中档来源:不详

答案

由题意设等差数列{an}的公差为d,则由求和公式可得
Sn=na1+
n(n-1)
2
d
,故
Sn
n
=a1+class="stub"n-1
2
d

S2007
2007
-
S2005
2005
=(a1+class="stub"2007-1
2
d
)-(a1+class="stub"2005-1
2
d

=d=2,故S2013=2013×(-2010)+class="stub"2013×2012
2
×2

=2013×(-2010)+2013×2012=2013×2=4026
故答案为:4026

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