已知数列{an}满足a1=3,a2=6,a(n+2)=2a(n+1)+3an,求an

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 04:22:16
已知数列{an}满足a1=3,a2=6,a(n+2)=2a(n+1)+3an,求an

已知数列{an}满足a1=3,a2=6,a(n+2)=2a(n+1)+3an,求an
已知数列{an}满足a1=3,a2=6,a(n+2)=2a(n+1)+3an,求an

已知数列{an}满足a1=3,a2=6,a(n+2)=2a(n+1)+3an,求an
用特征根法:因为a(n+2)=2a(n+1)+3an的特征方程是x-2x-3=0.解方程得x=3或x=﹣1.所有an=A×3^(n-1)+B×(-1)^(n-1).将a1=3,a2=6代入解得A=9/4 B=3/4 所以an=﹙9/4﹚×3^(n-1)+﹙3/4﹚×(-1)^(n-1).