等差数列{an}前n项和为sn且 s2013=-2013,a1008=3求s2014

问题描述:

等差数列{an}前n项和为sn且 s2013=-2013,a1008=3求s2014

设公差为d.S2013=(a1+a2013)×2013/2=2a1007×2013/2=-2013a1007=-1d=a1008-a1007=3-(-1)=4S2014=(a1+a2014)×2014/2=(a1007-1006d+a1007+1007d)×2014/2=(2a1007+d)×2014/2=[2×(-1)+4]×2014/2=2014