等差数列{an}中,Sn是其前n项和,a1=2008,S2007/2007-S2005/2005=-2,S2009=?

题目

等差数列{an}中,Sn是其前n项和,a1=2008,S2007/2007-S2005/2005=-2,S2009=?

答案

Sn=na1+n(n-1)d/2,则S2007/2007-S2005/2005=a1+1003d-a1-1002d=d=-2,
S2009=2009a1+2009(2009-1)d/2=2009×2008+2009×2008×(-2)/2=0