Question

令 X 和 Y 为下列等差数列的和： $Y - X$ 的值是多少？ $\begin{align*}X &= 10+12+14+\cdots+100,\\ Y &= 12+14+16+\cdots+102.\end{align*}$

Let X and Y be the following sums of arithmetic sequences: $\begin{align*}X &= 10+12+14+\cdots+100,\\ Y &= 12+14+16+\cdots+102.\end{align*}$ What is the value of $Y - X?$

$92$

$98$

$100$

$102$

$112$

答案：A

知识点：等差数列求和

难度评级：770

解答：

从 $12$ 到 $100$ 的所有偶数项在两个和中都出现，作差时会全部抵消。

因此 $Y - X = 102 - 10 = 92.$

所以正确答案是 A。

Note that the terms $12$ through $100$ are common to both sums. When we subtract, all these terms cancel out.

This means that $Y - X = 102 - 10 = 92.$

Thus, A is the correct answer.

2011 AMC 10A 第 4 题

答案：A

难度评级：770

解答：

其他年份的第 4 题