已知数列{an}的前n项和Sn=n^2-9n,第k项满足5＜ak＜8,则k等于

Sn=n^2-9n
S(n-1)=(n-1)^2-9(n-1)
=n^2-2n+1-9n+9
=n^2-11n+10
an=Sn-S(n-1)
=n^2-9n-(n^2-11n+10)
=n^2-9n-n^2+11n-10
=2n-10
ak=2k-10
5＜ak＜8
5＜2k-10＜8
15＜2k＜18
7.5＜k＜9
所以k=8