设等比数列an的公比为q前n项和为Sn若Sn+1,Sn,Sn+2成等数列,求q

设等比数列an的公比为q前n项和为Sn若Sn+1,Sn,Sn+2成等数列,求q
设等比数列an的公比为q前n项和为Sn若Sn+1,Sn,Sn+2成等数列,求q

设等比数列an的公比为q前n项和为Sn若Sn+1,Sn,Sn+2成等数列,求q
由题意得2sn=s(n+1)+s(n+2) 则s(n+1)-sn+(s(n+2)-sn)=0
即a(n+1)+a(n+2)+a(n+1)=0 则a(n+2)=-2a(n+1)
故q=-2