#### Question

What will be the nth term of an arithmetic progression if the sum of its n term is given by 2n^2+n

Collected in the board: Arithmetic sequence

Steven Zheng posted 12 hours ago

#### Answer

Since the sum of its n term is given by 2n^2+n

S_n = 2n^2+n

S_{n-1} =2 (n-1)^2-(n-1)

a_n = S_n-S_{n-1}

=2n^2+n-2(n-1)^2-(n-1)

=2n^2-2(n^2-2n+1)+1

=4n-1

Steven Zheng posted 12 hours ago

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