Question

等差数列{an}的前n项和为Sn,已知S6=36,Sn=324,S(n-6)=144(n>6),则n为多少?

Answer 1

因为Sn=324,s(n-6)=144

所以最后六项和=324-144=180=a(n-5)+a(n-4)+,+an

又S6=36=a1+a2+,+a6

两侧同时相加,有6(a1+an)=216

a1+an=36

Sn=n(a1+an)/2=n*36/2=324 知n=18