Question

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

Answer 1

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