设公比为q,等比数列,首项a1、公比q均不等于0
8a2+a5=0
8a1q+a1q^4=0
a1不等于0,等式两边同除以a1
q^4+8q=0
q(q^3+8)=0
q(q+2)(q^2-2q+4)=0
q不等于0,q^2-2q+4=(q-1)^2+3恒>0,要等式成立,只有q+2=0
q=-2
S5/S2=[a1(q^5 -1)/(q-1)]/[a1(q^2 -1)/(q-1)]
=(q^5 -1)/(q^2 -1)
=(-32-1)/(4-1)
=-33/3
=-11