已知数列{an},a1=1,a(n-1)=2(a1+a2+a3+...+an),求通项公式

a(n-1)=2[a(1)+a(2)+...+a(n)],a(1)=a(2-1)=2[a(1)+a(2)],a(2)=-a(1)/2=-1/2.
a(n)=2[a(1)+a(2)+...+a(n)+a(n+1)],
a(n)-a(n-1)=2[a(n+1)],
xa(n)-a(n-1)=y[xa(n+1)-a(n)],xy=2,x+y=1,y=1-x,2=x(1-x)=x-x^2,
0=x^2-x+2,1^2-8=-7,x=[1+i7^(1/2)]/2,y=[1-i7^(1/2)]/2,1/y=x/2
xa(n+1)-a(n)=x[xa(n)-a(n-1)]/2,
{xa(n+1)-a(n)}是首项为xa(2)-a(1)=-x/2-1,公比为(x/2)的等比数列。
xa(n+1)-a(n)=-(x/2+1)*(x/2)^(n-1),
xy^(n-1)a(n+1)-y^(n-1)a(n)=-(x/2+1),
b(n)=y^(n-1)a(n),
(x/y)b(n+1)-b(n)=-(x/2+1),
[b(n+1)+z] = (y/x)[b(n)+z], -(x/2+1)y/x = z[y/x-1] = z(y-x)/x,
z=-(x/2+1)y/(y-x),
{b(n)-(x/2+1)y/(y-x)}是首项为b(1)-(x/2+1)y/(y-x)=a(1)-(x/2+1)y/(y-x)=1-(x/2+1)y/(y-x)=-x[1+y/2]/(y-x),公比为(y/x)的等比数列。
b(n)-(x/2+1)y/(y-x)=-x(1+y/2)/(y-x)*(y/x)^(n-1),
b(n)=y^(n-1)a(n)=(x/2+1)y/(y-x)-x(1+y/2)/(y-x)*(y/x)^(n-1),
a(n)=(x/2+1)y^(n-2)/(y-x)-x(1+y/2)/(y-x)*(1/x)^(n-1)
=(x/2+1)y^(n-2)/(y-x)-(1+y/2)y^(n-2)/[(y-x)2^(n-1)]

x/2+1=[1+i7^(1/2)]/4+1=[5+i7^(1/2)]/4,