已知{an}是以a为首项,q为公比的等比数列,Sn为它的前n项和,当S1、S3、S4成等差数列时,求q的值

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s1=a
s3=a(1-q^3)/(1-q)
s4=a(1-q^4)/(1-q)
当S1、S3、S4成等差数列时
2s3=s1+s4
a(1-q^3)/(1-q)=a+a(1-q^4)/(1-q)
(1-q^3)/(1-q)=1+(1-q^4)/(1-q)
(1-q)(1+q+q^2)/(1-q)=1+(1+q)(1-q)(1+q^2)/(1-q)
1+q+q^2=1+(1+q)(1+q^2)
q+q^2=(1+q)(1+q^2)
q(1+q)=(1+q)(1+q^2)
(1+q)(1+q^2)-q(1+q)=0
(1+q)(1-q+q^2)=0
1+q^3=0
q^3=-1
q=-1

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