Question

求An的题目：若数列AN的前N项和为SN=n^2-2n+2,求数列AN 的通项,并判断是否为等差数列

Answer 1

An=Sn-S(n-1)

=n²-2n+2-[(n-1)²-2(n-1)+2]

=2n-1-2

=2n-3

n=1时 A1=S1=1 2n-3= -1 1≠-1 所以An不是等差数列

An= 1 (n=1)

=2n-3 (≥2)