Which of the following could be the sum of nine consecutive integers?

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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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