(2014•河西区三模)设Sn为等比数列{an}的前n项和,8a2+a5=0,则S5S2等于(  ) A.11 B.5 C.-8 D.-11

问题描述:

(2014•河西区三模)设Sn为等比数列{an}的前n项和,8a2+a5=0,则

S5
S2
等于(  )
A. 11
B. 5
C. -8
D. -11

设等比数列{an}的公比为q,(q≠0)
由题意可得8a2+a5=8a1q+a1q4=0,解得q=-2,

S5
S2
=
a1(1−q5)
1−q
a1(1−q2)
1−q
=
1−q5
1−q2
=
1−(−2)5
1−(−2)2
=-11
故选D