Question

在八项数列 $A$ 、 $B$ 、 $C$ 、 $D$ 、 $E$ 、 $F$ 、 $G$ 、 $H$ 中， $C$ 的值为 $5$ ，并且任意三个连续项之和为 $30$ 。 $A+H$ 是多少？

In the eight term sequence $A,$ $B,$ $C,$ $D,$ $E,$ $F,$ $G,$ $H,$ the value of $C$ is $5$ and the sum of any three consecutive terms is $30.$ What is $A+H?$

$17$

$18$

$25$

$26$

$43$

答案：C

知识点：递推找规律

难度评级：1370

解答：

由题设得到同理， $A + B + C = 30$ $B = 25 - A.$ $B + C + D = 30$ $D = A.$

继续对每三个连续项应用同一条件，得到最后 $H = 25 - A$ 。 $E = 25 - A, F = 5, G = A,$

因此所求和为 $A + 25 - A = 25.$

所以正确答案是 C。

From the condition about the sequence, we get that $A + B + C = 30$ $B = 25 - A.$ Similarly, we get $B + C + D = 30$ $D = A.$

Propagating these values through the sequence and repeating the condition for every consecutive triple, we get that $E = 25 - A, F = 5, G = A,$ and finally, $H = 25 - A.$

The desired sum is then $A + 25 - A = 25.$

Thus, C is the correct answer.

2011 AMC 10A 第 17 题

答案：C

难度评级：1370

解答：

其他年份的第 17 题