{an}的前几项和为Sn=32n-n²,求证{an}为等差数列

{an}的前几项和为Sn=32n-n²,求证{an}为等差数列
{an}的前几项和为Sn=32n-n²,求证{an}为等差数列

{an}的前几项和为Sn=32n-n²,求证{an}为等差数列
Sn=32n-n^2
S(n-1)=32n-32-(n-1)^2
=34n-n^2-33
Sn-S(n-1)=an
=32n-n^2-(34n-n^2-33)
=-2n+33
所以它就是公差为2的等差数列