数列an=2a(n-1)+2^n+(-1),a1=5,若{(an+p)/2^n}为等差数列,求实数p

题目

数列an=2a(n-1)+2^n+(-1),a1=5,若{(an+p)/2^n}为等差数列,求实数p
标准答案是-1

答案

an=2a(n-1)-1 +2^n
an -1 = 2(a(n-1) -1 ) + 2^n
(an-1)/2^n - (a(n-1) -1)/2^(n-1) = 1
p= -1