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...

题目

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.

答案

(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