(1/2)已知{an}的前n项和为Sn,a1=1.且3an-1+2Sn=3求a1,a2的值,并求数列{an}的通项公式. （注：式中...(1/2)已知{an}的前n项和为Sn,a1=1.且3an-1+2Sn=3求a1,a2的值,并求数列{an}的通项公式.（注：式中的n,n-

3an-1+2Sn=3 （1） 3an+2Sn+1=3 (2) (2)--(1) 得 2an+1+3an-an-1
特征方程2X^2+3X-3=0 得X1，X2，
则an=a*x1^(n-1)+b*x2^(n-1)
a1=1,a2=-1
1=a+b,-1=a*x1+b*x2.
得a，b。

a1=1,
a2=1/3
an=1/[3^(n-1)]

首先,an=sn-s（n-1）,代入原式,
并移项得3sn-3s(n-1)+2sn=4,
5sn-3s(n-1)=45sn-10=3(n1)-6
5(sn-2)=3[s(n-1)-2]
故数列{sn-2}是首项
s1-2=a1-2=-1,公比为5/3的等比数列
由等比数列通项公式,sn-2=（-1）

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