解释下设辅助数列法求An An+1=pAn+q

设a(1)=a.
p=1时,a(n+1)=a(n) + q,{a(n)}是首项为a(1)=a,公差为q的等差数列.a(n) = a + (n-1)q.
p不为1时,a(n+1) = pa(n) + q,
a(n+1) + q/(p-1) = pa(n) + q + q/(p-1) = pa(n) + pq/(p-1) = p[a(n) + q/(p-1)],
{a(n) + q/(p-1)}是首项为a(1)+q/(p-1) = a + q/(p-1),公比为p的等比数列.
a(n) + q/(p-1) = [a+q/(p-1)]p^(n-1),
a(n) = [a + q/(p-1)]p^(n-1) - q/(p-1)