In how many ways can 90 be written as the sum of two or more consecutive even positive integers that are arranged in increasing order ?

A. 1

B. 2

C. 3

D. 4

E. 5

1. 2026 AMC 8 官方解析

设最小偶数为$a$、共有$n$个偶数.
$a + a + 2 + a + 4 + \cdots + a + 2(n - 1) = 90$
$[a + a + 2(n - 1)] \times n \div 2 = 90$
$(a + n - 1) \times n = 90$
$a + n - 1 > n$ , 且$a + n - 1 , n$奇偶性不同 ,
$(a + n - 1) \times n = 90$
$45 \times 2$ , $n = 2$ , $a = 44$
$30 \times 3$ , $n = 3$ , $a = 28$
$18 \times 5$ , $n = 5$ , $a = 14$
$15 \times 6$ , $n = 6$ , $a = 10$
$10 \times 9$ , $n = 9$ , $a = 2$