(1) Given that the sum of the first n terms of the sequence an is Sn, satisfying Sn = an & # 178; + BN, it is proved that an is an arithmetic sequence (2) It is known that the sum of the first n terms of the arithmetic sequence an is Sn, and it is proved that Sn / N is also an arithmetic sequence

(1) Given that the sum of the first n terms of the sequence an is Sn, satisfying Sn = an & # 178; + BN, it is proved that an is an arithmetic sequence (2) It is known that the sum of the first n terms of the arithmetic sequence an is Sn, and it is proved that Sn / N is also an arithmetic sequence

Sn=an²＋bn
Then:
When n = 1, A1 = S1 = a + B
When n ≥ 2, an = SN-S (n-1) = [an & # 178; + BN] - [a (n-1) &# 178; + B (n-1)] = 2An - (a-b), where n ≥ 2
When n = 1, it also satisfies the above equation
It is shown that an = 2An - (a-b)
When n ≥ 2, an-a (n-1) = 2A = constant
Then the sequence {an} is an arithmetic sequence
Sn/n=an＋n
Then: [S (n + 1) / (n + 1)] - [Sn / N] = a = constant
The sequence {Sn / N} is also an arithmetic sequence