AMC8 2002

AMC8 2002 · Q3

AMC8 2002 · Q3. It mainly tests Averages (mean), Arithmetic sequences basics.

What is the smallest possible average of four distinct positive even integers?

四个不同的正偶整数的最小可能平均数是多少？

(A) 3 3

(B) 4 4

(D) 6 6

(E) 7 7

Answer

Correct choice: (C)

正确答案：（C）

Solution

The smallest average will occur when the numbers are as small as possible. The four smallest distinct positive even integers are 2, 4, 6, and 8 and their average is 5. Note: These numbers form an arithmetic sequence. The average of the numbers in any arithmetic sequence is the average of the first and last terms.

为了使平均数最小，数字应尽可能小。四个最小的不同正偶整数是2、4、6和8，它们的平均数是5。注意：这些数字构成一个等差数列。任何等差数列中数字的平均数等于首尾项的平均数。

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