已知{an}是等差数列,公差d不等于0,且a1 a3 a13成等比数列,sn是{an}的前n项和,（1）求证s1 s2 s9成...已知{an}是等差数列,公差d不等于0,且a1 a3 a13成等比数列,sn是{an}的前n项和,（1）求证s1 s2 s9成等比数列；（2）若s3=9,an=21求n.
问题描述：
已知{an}是等差数列,公差d不等于0,且a1 a3 a13成等比数列,sn是{an}的前n项和,（1）求证s1 s2 s9成...
已知{an}是等差数列,公差d不等于0,且a1 a3 a13成等比数列,sn是{an}的前n项和,（1）求证s1 s2 s9成等比数列；（2）若s3=9,an=21求n.
答
（1） (a3)^2=a13*a1
(a1+2d)^2=(a1+12d)*a1
已知d0
d=2a1
s1=a1
s3=3a1+3d=9a1
s9=9a1+36d=81a1
(s3)^2=s1*s9
所以s1 s3 s9成等比数列
（2）s3=9a1=9,a1=1,d=2a1=2
an=2n-1
21=2n-1
2n=22 n=11
答
(a3)^2=a13*a1(a1+2d)^2=(a1+12d)*a1d-2a1=0d=2a1s1=a1s3=3a1+3d=9a1s9=9a1+36d=81a1(s3)^2=s1*s9,所以s1 s3 s9成等比数列s3=9a1=9,a1=1,d=2a1=2an=2n-121=2n-12n=22n=11