等差数列an的公差不为0,首项a1=-12,若a1,a3,a4,a5组成一个等比数列,求Sn

问题描述:

等差数列an的公差不为0,首项a1=-12,若a1,a3,a4,a5组成一个等比数列,求Sn

解析:设数列{an}的公差为d,那么:a3=a1+2d,a4=a1+3d,a5=a1+4d若a1,a3,a4,a5组成一个等比数列,那么:a3/a1=a5/a4即a3*a4=a1*a5所以:(a1+2d)(a1+3d)=a1*(a1+4d)a1²+5a1*d+6d²=a1²+4a1*d6d²+a1*d...