设等比数列{an}的前n项和为Sn,已知a1=2011,且an+2an+1+an+2=0,则S2012=?

设等比数列{an}的前n项和为Sn,已知a1=2011,且an+2an+1+an+2=0,则S2012=?
设等比数列{an}的前n项和为Sn,已知a1=2011,且an+2an+1+an+2=0,则S2012=?

设等比数列{an}的前n项和为Sn,已知a1=2011,且an+2an+1+an+2=0,则S2012=?
由题设可知:
(a1)+2(a2)+(a3)=0
可设公比=q.
a2=qa1.a3=q²a1
∴(a1)(1+2q+q²)=0
∴(q+1)²=0
∴q=-1
∴S2012=(a1){[(-1)^2012]-1}/(-1-1)=0