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=

3
2
,S3=
9
2
,则公比q=(  )
A. 1或-
1
2

B. -
1
2

C. 1
D. -1或
1
2

∵a3=

3
2
,S3=
9
2

①当q=1时,S3
9
2
3
2
×3
,满足条件.
②当q≠1时,可得
a1q2
3
2
a1(q3−1)
q−1
9
2
.解得
a1=6
q=−
1
2

综上可知:q=1或-
1
2

故选:A.