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

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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

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
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

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