2S(n+1)=Sn+S(n-1)
2Sn=S(n-1)+S(n-2)
...
2S3=S2+S1
两边相加得：
2S(n+1)+2Sn=Sn+2S2+S1
2S(n+1)+Sn=2S2+S1
S1=a1=2
S2=a1+a2=5
2S(n+1)+Sn=12
2(S(n+1)-4)=-(Sn-4)
(S(n+1)-4)/(Sn-4)=-1/2
{Sn-4}是公比为-1/2的等比数列
Sn-4=(S1-4)*(-1/2)^(n-1)=-2*(-1/2)^(n-1)
S(n-1)-4=-2*(-1/2)^(n-2)
n>1时
an=Sn-S(n-1)
=-2*(-1/2)^(n-1)+2*(-1/2)^(n-2)
=2*(-1/2)^(n-2)(1/2+1)
=3(-1/2)^(n-2)
n=1时,a1=2