如果一个数列{an}满足a1=3,an+1=an如果一个数列{An}满足A1=3,An+1=An+4n,那么A100是

Question

如果一个数列{an}满足a1=3,an+1=an
如果一个数列{An}满足A1=3,An+1=An+4n,那么A100是

Answer 1

An+1=An+4n
则A100=A99+4X99
A99=A98+4X98
.
A3=A2+4X2
A2=A1+4X1
以上各式相加得A100=A1+4X99+4X98...+4X2+4X1
A100=3+4(1+2+...+99)
=3+4x50x99
=19803