已知数列{an}满足:a1=3,an=Sn-1+2n,求数列an及sn

题目

已知数列{an}满足:a1=3,an=Sn-1+2n,求数列an及sn

答案

An-An-1=Sn-1+2n-Sn-2+2n+2=An-1+2
即 An=2An-1+2
变换得：An+2=2*（An-1+2）
令An+2=Bn,An-1+2=Bn-1
结果：An=9*2^(n-2)-2,A1=3
Sn=9*2^(n-1)-4n