{an}是公比为q的等比数列,且-a5,a4,a6成等差数列,则q=

题目

{an}是公比为q的等比数列,且-a5,a4,a6成等差数列,则q=

答案

2a4=-a5+a6
2a4=-a4q+a4q^2
2a4=-a4q+a4q^2
a4q^2-a4q-2a4=0
a4(q^2-q-2)=0
a4(q-2)(q+1)=0
(q-2)(q+1)=0
q=2或q=-1