2014 AMC 10A 第 10 题

Question

从

a

开始的五个连续正整数的平均数为

b

。从

b

开始的

5

个连续整数的平均数是多少？

Five positive consecutive integers starting with

a

have average

b.

What is the average of

5

consecutive integers that start with

b?

a+3

a+4

a+5

a+6

a+7

答案：B

知识点：等差数列平均数

难度评级：900

小提示：

从

x

开始的五个连续整数的平均数是

x+2

。

The average of five consecutive integers starting at

x

is

x+2

大提示：

先对

a

用这个规则，再对

b

用一次。

Apply that rule first to

a

, then to

b

解答：

从

x

开始的

5

个连续整数的平均数为

\dfrac{5x + 1 + 2 + 3 + 4}{5} = x + 2\text{。}

因此，从

a

开始的

5

个连续整数的平均数为

a + 2

，也就是

b

。

从

b

开始的

5

个连续整数的平均数为

b + 2 = a + 4\text{。}

所以正确答案是 B。

Note that the average of

5

consecutive numbers starting with

x

is

\dfrac{5x + 1 + 2 + 3 + 4}{5} = x + 2.

This means that the average of

5

consecutive integers starting with

a

is

a + 2,

which we know is

b.

Furthermore, the average of

5

consecutive numbers starting with

b

is

b + 2 = a + 4.

Thus, B is the correct answer.

2014 AMC 10A 第 10 题

答案：B

难度评级：900

小提示：

大提示：

解答：

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