已知{an}是公差不为0的等差数列,其前n项和为sn,其中a1,a3,a6成等比数列,且s5=60,求an和sn

题目

已知{an}是公差不为0的等差数列,其前n项和为sn,其中a1,a3,a6成等比数列,且s5=60,求an和sn

答案

a3=a1+2d,a6=a1+5d因为a1,a3,a6成等比数列,所以a3^2=a1a6,所以（a1+2d）^2=a1（a1+5d）展开的a1^2+4a1d+4d^2=a1^2+5a1d,则a1d=4d^2,因为公差不为0,所以约去d,得d=4a1s5=5a1+10d=45a1=60,所以a1=4/3,d=16/3则an=4/3+(...