等比数列{an},a3,a5,a6成等差数列,求a11-(a9+a10)的值

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等比数列{an},a3,a5,a6成等差数列,求a11-(a9+a10)的值
等比数列{an},a3,a5,a6成等差数列,求a11-(a9+a10)的值

等比数列{an},a3,a5,a6成等差数列,求a11-(a9+a10)的值
等比数列
a3=a1*q^2
a5=a1*q^4
a6=a1*q^5
a3,a5,a6成等差数列,
2a1*q^4=a1*q^2+a1*q^5 a1,q≠0
q^3-2q^2+1=0
q^2(q-1)-(q-1)(q+1)=0
(1)q=1 an=a1 a11-(a9+a10)=-a1
(2)q^2-q-1=0 a11-(a9+a10)=a9(q^2-q-1)=0