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Which of the following could be the sum of nine consecutive integers?A、29B、46C
Which of the following could be the sum of nine consecutive integers?A、29B、46C
游客
2025-02-23
31
管理
问题
Which of the following could be the sum of nine consecutive integers?
选项
A、29
B、46
C、57
D、99
E、100
答案
D
解析
设9个连续整数分别为月,n+1,n+2,…,n+8。根据等差数列求这9个数的和:n+n+1+n+2+…+n+8=(n+n+8×9)/2=9(n+4),得出任意9个连续整数的和必然是9的倍数。选项中只有99是9的倍数,所以选择D选项。
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