已知数列{an}中,a1=20,an+1=an+2n-1,n∈N*,则数列{an}的通项公式an=_.
问题描述:
已知数列{an}中,a1=20,an+1=an+2n-1,n∈N*,则数列{an}的通项公式an=______.
答
因为数列{an}中,a1=20,an+1=an+2n-1,n∈N*,所以a2=a1+1,a3=a2+3,a4=a3+5,…an=an-1+2n-3;上式累加可得:an=a1+1+3+5+…+(2n-3)=20+n-1+(n−1)(n−2)2× 2=n2-2n+21.故答案为:n2-2n+21....