设等比数列｛an｝的公比为q,前n项和为Sn,若Sn+1,Sn,Sn+2成等差数列,则q=?

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设等比数列｛an｝的公比为q,前n项和为Sn,若Sn+1,Sn,Sn+2成等差数列,则q=?
答案是-2或1

因为Sn+1,Sn,Sn+2成等差数列
S(n+1)+S(n+2)=2*S(n)
(q^(n+1)-1)*a1/(q-1)+(q^(n+2)-1)*a1/(q-1)=2*(q^(n)-1)*a1/(q-1)
q^(n+1)-1+q^(n+2)-1=2*q^n-2
q*q+q-2=0
所以q=-2或1

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