设数列 {an} 的前 n 项和为 Sn,则 {an} 等差。

(1) S n4=n 2+2n, n=1,2,3

(2) S n4=n 2+ 2n +1,n=1,2,3

A、条件(1)充分,但条件(2)不充分
B、条件(2)充分,但条件(1)不充分
C、条件(1)和(2)单独都不充分,但条件(1)和条件(2)联合起来充分
D、条件(1)充分,条件(2)也充分
E、条件(1)和(2)单独都不充分,但条件(1)和条件(2)联合起来也不充分
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正确答案:

A

答案解析:

等差数列的前n项和公式为Sn=An2+Bn,A、B为全体实数,因此条件(1)充分,条件(2)不充分,选A。

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