已知一等差数列的前n项和为Sn=2n^2-n,则an=?

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已知一等差数列的前n项和为Sn=2n^2-n,则an=?
已知一等差数列的前n项和为Sn=2n^2-n,则an=?

已知一等差数列的前n项和为Sn=2n^2-n,则an=?
Sn=2n^2-n
S(n-1)=2(n-1)^2-(n-1)=2n^2-5n+3
an=Sn-S(n-1)=4n-3
a1=s1=2-1=1
符合an=4n-3
所以an=4n-3

sn=n[a1+a1+(n-1)d]/2
=d/2*n^2+(a1-d/2)*n
=2n^2-n
d/2=2,a1-d/2=-1
d=4,a1=1
an=1+(n-1)*4=4n-3

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