Sn represent the sum of n terms of a certain sequence, where each term after the first term of the sequence is obtained by adding a constant c, where c

题目

S_n represent the sum of n terms of a certain sequence, where each term after the first term of the sequence is obtained by adding a constant c, where c > 0, in the preceding term

Quantity A

S_n+1

Quantity B

S_n+2

选项

The quantity in Column A is greater.

The quantity in Column B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

解析

要理解这道题的解法，请先仔细读题： S_n 表示某数列的前 n 项和，该数列中从第二项起，每一项都由前一项加上一个正的常数 c（c>0）得到。 **情况1：** 因为 c 为正，我们取 c=1，并设数列的首项为 -10。此时数列为：-10, -9, -8, -7, ... 因为 S_n 是数列的和，所以 S_1 = -10，S_2 = -19。此时 S_1 > S_2。 **情况2：** 同样取 c=1，并设数列的首项为 1。此时数列为：1, 2, 3, 4, ... 因为 S_n 是数列的和，所以 S_1 = 1，S_2 = 3。此时 S_2 > S_1。因此，答案为 **D**。

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