因前三项成等差数列,设a2=a,公差为d,
则,a1=a-d,a2=a,a3=a+d.
∴ a1+a2+a3=a-d+a+a+d=3a.---(1)
因后三项成等比数列,设其公比为q,
则,a2=a,a3=aq,a4=aq^2.
∴a2++a3+a4=a(1+q+q^2).
=a[1+√3+(√3)^2.]
∴a2+a3+a4=(4+√3)a.---(2)
(a1+a2+a3)/(a2+a3+a4)=3a/(4+√3)a.
=3(4-√3)/(4+√3)(4-√3)
=3(4-√3)/13.
∴ (a1+a2+a3)/(a2+a3+a4)=3(4-√3)/13.