Given that the sum of the first n terms of the sequence {an} is Sn = n & # 178; + n & # 189; N, find the general term formula of the sequence

Given that the sum of the first n terms of the sequence {an} is Sn = n & # 178; + n & # 189; N, find the general term formula of the sequence

Sn = n² + 1/2 * n
S(n-1) = (n-1)² + 1/2 * (n-1)
an = Sn - S(n-1)
= n² + 1/2 * n - (n-1)² - 1/2 * (n-1)
= n² - (n-1)² + 1/2 * n - 1/2 * n + 1/2
= (n + n - 1)(n - n + 1) + 1/2
= 2n - 1/2
an - a(n-1) = (2n - 1/2) - { 2(n-1) - 1/2 } = 2
Is an arithmetic sequence with a tolerance of 2
If you are satisfied with my answer,
Friends who ask questions from mobile phones can click "satisfied" in the upper right corner of the client!