What is the sum of the terms in a certain sequence of consecutive integers?(1) The least term in the sequence is 8

题目

What is the sum of the terms in a certain sequence of consecutive integers?

(1) The least term in the sequence is 8.

(2) The average of (arithmetic mean) terms is 16.

选项

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

解析

我们已知该数列为**连续数列**，因此解题关键通常是确定数列的**项数**以及**首项**（或其他参考项，比如第二项）。 **条件1**：无法确定数列有多少项，**不充分**。 **条件2**：无法确定数列有多少项，**不充分**。 **联立两个条件**：此时我们可确定数列**首项为8**。由于数列的平均数为16，那么数列的**最大值**必然是16 + (16 - 8) = 24。至此我们已明确该数列的全部关键信息，可计算出所有项的和，**充分**。 **答案：C**

在线客服

官方微信

公众号