1.(3-p)sn+2p(sn-s(n-1))=p+3
(3+p)sn=2ps(n-1)+p+3
sn=2p/(p+3)s(n-1)+1
an+s(n-1)=2p/(p+3)s(n-1)+1
an=(p-3)/(p+3)s(n-1)+1
a(n-1)=(p-3)/(p+3)s(n-2)+1
an-a(n-1)=(p-3)/(p+3)(s(n-1)-s(n-2))
an-a(n-1)=(p-3)/(p+3)a(n-1)
an=2p/(p+3)a(n-1)
所以an為公比為2p/(p+3)的等比數(shù)列.
2.f(p)=2p/(p+3)
f(b(n-1))=2b(n-1)/(b(n-1)+3)
bn=3b(n-1)/(b(n-1)+3)
1/bn=1/3+1/b(n-1)
1/bn-1/b(n-1)=1/3
所以1/bn為等差數(shù)列,公差為1/3,首項(xiàng)為1/b1=1/a1,
1/bn=1/a1+(n-1)/3=(3+a1(n-1))/3*a1
bn=3a1/(3+a1(n-1))