> 数学 >
等差数列{an}中,Sn是其前n项和,a1=−2008,
S2007
2007
S2005
2005
=2,则S2008
=______.
人气:312 ℃ 时间:2020-04-18 18:40:56
解答
∵在等差数列中S2n-1=(2n-1)an
S2007
2007
=a1004
S2005
2005
=a1003
又∵
S2007
2007
S2005
2005
=2

∴d=2,又由a1=-2008
Sna1n+
n(n−1)
2
d
=n2-n-2008n,
∴S2008=-2008
故答案为:-2008
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