由公差d=2，得到a_n=a₁+2（n-1）=2n+a₁-2，S_n=na₁+

n(n−1)

2

×2=n²+n（a₁-1）
则

lim

n→∞

a 2n −n2

Sn

=

lim

n→∞

3n2+4(a1−2)n+(a1−2)2

n2+n(a1−1)

=

lim

n→∞

3+ 4(a1−2) n + (a1−2)2 n2

1+ a1−1 n

=3
故答案为3．