AMC12 2014 A

AMC12 2014 A · Q9

AMC12 2014 A · Q9. It mainly tests Sequences & recursion (algebra), Averages (mean).

Five positive consecutive integers starting with $a$ have average $b$. What is the average of $5$ consecutive integers that start with $b$?

以$a$开始的5个连续正整数的平均数是$b$。以$b$开始的5个连续整数的平均数是多少？

(A) \ a+3 \ a+3

(B) \ a+4 \ a+4

(D) \ a+6 \ a+6

(E) \ a+7 \ a+7

Answer

Correct choice: (B)

正确答案：（B）

Solution

Let $a=1$. Our list is $\{1,2,3,4,5\}$ with an average of $15\div 5=3$. Our next set starting with $3$ is $\{3,4,5,6,7\}$. Our average is $25\div 5=5$. Therefore, we notice that $5=1+4$ which means that the answer is $\boxed{\textbf{(B)}\ a+4}$.

设$a=1$，则数列为$\{1,2,3,4,5\}$，平均数$15\div 5=3$。以3开始的数列为$\{3,4,5,6,7\}$，平均数$25\div 5=5$。注意到$5=1+4$，故答案为$\boxed{\textbf{(B)}\ a+4}$。

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