问题
填空题
等比数列{an}的前n项和为Sn,已知S1,2S2,3S3成等差数列,则{an}的公比为______.
答案
∵等比数列{an}的前n项和为Sn,已知S1,2S2,3S3成等差数列,
∴an=a1qn-1,又4S2=S1+3S3,即4(a1+a1q)=a1+3(a1+a1q+a1q2),
解q=
.1 3
故答案为1 3
等比数列{an}的前n项和为Sn,已知S1,2S2,3S3成等差数列,则{an}的公比为______.
∵等比数列{an}的前n项和为Sn,已知S1,2S2,3S3成等差数列,
∴an=a1qn-1,又4S2=S1+3S3,即4(a1+a1q)=a1+3(a1+a1q+a1q2),
解q=
.1 3
故答案为1 3