在数列an中,a1=1,且满足a(n+1)=3an +2n,求an
问题描述:
在数列an中,a1=1,且满足a(n+1)=3an +2n,求an
答
两边加n+1,得a"+n+1=3(a'+n)+1;令bn=an+n,得b"=3b'+1,得(b"+1/2)=3(b'+1/2)数列{bn+1/2}是等比数列,得bn=5/2*3^(n-1)-1/2,故an=5/2*3^(n-1)-1/2-n