已知数列{an}的前n项和Sn=n2-9n,第k项满足5<ak<8,则k等于(  ) A.9 B.8 C.7 D.6

问题描述:

已知数列{an}的前n项和Sn=n2-9n,第k项满足5<ak<8,则k等于(  )
A. 9
B. 8
C. 7
D. 6

an=

S1(n=1)
SnSn−1(n≥2)

=
−8(n=1)
−10+2n(n≥2)

∵n=1时适合an=2n-10,∴an=2n-10.
∵5<ak<8,∴5<2k-10<8,
15
2
<k<9,又∵k∈N+,∴k=8,
故选B.