已知等比数列{an}的前n项和为Sn,a3=32,S3=92,则公比q=( ) A.1或-12 B.-12 C.1 D.-1或12
问题描述:
已知等比数列{an}的前n项和为Sn,a3=
,S3=3 2
,则公比q=( )9 2
A. 1或-
1 2
B. -
1 2
C. 1
D. -1或
1 2
答
∵a3=
,S3=3 2
,9 2
①当q=1时,S3=
=9 2
×3,满足条件.3 2
②当q≠1时,可得
.解得
a1q2=
3 2
=
a1(q3−1) q−1
9 2
.
a1=6 q=−
1 2
综上可知:q=1或-
.1 2
故选:A.