Question

a1=2,a(n+1)+an=3•2^n求通项公式

Answer 1

A(n+1) = 3*2^n - An

A(n+1) - 2^(n+1) = 3*2^n - 2^(n+1) - An

= (3 - 2)*2^n - An

= -1 *(An - 2^n)

由此可知,｛An - 2^n｝是一个比值为 （-1）的等比数列.

所以有：

An - 2^n = (-1)^(n-1) * (A1 - 2^1) = 0

即 An = 2^n