已知数列{an}的前n项和Sn=n(2n+1)求改数列的通项公式判断39是改数列的第几项

Question

已知数列{an}的前n项和Sn=n(2n+1)求改数列的通项公式 判断39是改数列的第几项

Answer 1

sn=n(2n+1)=2n^2+n
sn-1=(n-1)(2(n-1)+1)
=(n-1)(2n-2+1
=(n-1)(2n-1)
=2n^2-n-2n+1
=2n^2-3n+1
Sn-Sn-1=
an=2n^2+n-(2n^2-3n+1)
=2n^2+n-2n^2+3n-1
=4n-1
4n-1=39
4n=40
n=10
是第10项