已知递增数列{An}满足a1=1,2a(n+1)=An+a(n+2),n∈N+,且a1,a2,a4成等比.
问题描述:
已知递增数列{An}满足a1=1,2a(n+1)=An+a(n+2),n∈N+,且a1,a2,a4成等比.
1.求:An.
2.若数列{Bn}满足:B(n+1)=3Bn+2^An,且n∈N+,B1=1.
(1).求:Bn.
(2).设Cn=An(3^n-Bn),求数列{Cn}的前n项和Sn.
答
(1) 由2A(n+1)=An+A(n+2),则为等差数列,设为An=A1+(n-1)*d,则A2=1+d,A4=1+3d,由A1、A2、A4成等比数列,A2*A2=A1*A4,(1+d)*(1+d)=(1)*(1+3d),d=1或0,递增数列取正值d=1,则An=n,即为1,2,3,4,.(2)B(n+1)=3Bn+2^n,变换...