设数列{an}是公差不为0的等差数列,Sn是数列{an}的前n项和,若S1,S2,S4成等比数列,则a4/a1=?

问题描述:

设数列{an}是公差不为0的等差数列,Sn是数列{an}的前n项和,若S1,S2,S4成等比数列,则a4/a1=?
如题

∵(S2)^2=S1*S4∴(a1+a2)^2=a1(a1+a2+a3+a4)=> (2a1+d)^2=a1(4a1+6d)=>4(a1)^2+4a1d+d^2=4(a1)^2+6a1d=>d^2=2a1d∴d=2a1a4=a1+3d=a1+6a1=7a1所以a4/a1=7a1/a1=7哪里不理解的话可以追问