Question

数列{an}满足递推公式an=3a（n-1）【角标】+3^n+1,又a1=5,则使数列{an+拉姆的/3^n}为等差数列

Answer 1

λ=1/2,下面是理由

设an-μ=3(a(n-1)-μ) 3^n移项得an=3a(n-1) 3^n-2μ,即μ=-1/2

故an 1/2=3(a(n-1) 1/2) 3^n

等式两边同时除以3^n,可得

(an 1/2)/3^n=(a(n-1) 1/2)/3^(n-1) 1

所以数列{(an 1/2)/3^n}为等差数列,公差为1