设an是公比为q的等比数列,Sn是它的前n项的和,若S(n+1),Sn,S(n+2)成等差数列,则公比q=

设an是公比为q的等比数列,Sn是它的前n项的和,若S(n+1),Sn,S(n+2)成等差数列,则公比q=
设an是公比为q的等比数列,Sn是它的前n项的和,若S(n+1),Sn,S(n+2)成等差数列,则公比q=

设an是公比为q的等比数列,Sn是它的前n项的和,若S(n+1),Sn,S(n+2)成等差数列,则公比q=
S(n+1),Sn,S(n+2)成等差数列,有
2Sn=S(n+1)+S(n+2)
2Sn=Sn+a(n+1)+Sn+a(n+1)+a(n+2)
有a(n+2)+2a(n+1)=0,a(n+2)=a(n+1)*q
所以两边同时除a(n+1)
q+2=0,q=2