问题
选择题
(理科)设等比数列{an}的前n项和为Sn,已知a1=2,且an+2an+1+an+2=0(n∈N*),则S2010=( )
A.2
B.0
C.-2
D.200
答案
∵an+2an+1+an+2=0
∴an+2anq+anq2=0即1+2q+q2=0
∴q=-1
S2010=
=02(1-(-1)2010) 1-(-1)
故选B
(理科)设等比数列{an}的前n项和为Sn,已知a1=2,且an+2an+1+an+2=0(n∈N*),则S2010=( )
A.2
B.0
C.-2
D.200
∵an+2an+1+an+2=0
∴an+2anq+anq2=0即1+2q+q2=0
∴q=-1
S2010=
=02(1-(-1)2010) 1-(-1)
故选B