Question

在八项数列 $A, B, C, D, E, F, G, H$ 中， $C$ 的值为 $5$ ，且任意三个连续项的和为 $30$ 。求 $A + H$ ？

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 $A + H?$

$17$

$18$

$25$

$26$

$43$

因为 $A + B + C = B + C + D = 30$ ，所以 $D = A$ ；同理可知，这个数列以 $3$ 为周期重复。因此第八项 $H$ 等于 $B$ 。

由 $A + B + C = 30$ 且 $C = 5$ ，得 $A + H = A + B = 30 - 5 = 25$ 。

因此，正确答案是 C。

Since $A + B + C = B + C + D = 30,$ we get $D = A,$ and likewise the sequence repeats with period $3.$ Thus $H,$ the eighth term, equals $B.$

From $A + B + C = 30$ and $C = 5,$ we have $A + H = A + B = 30 - 5 = 25.$

Thus, the correct answer is C.