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29個連續整數的合是1537其中最小的整數是多少
A)33 B)39 c)41D)44?
問題： 29 個連續整數的合是 1537，其中最小的整數是多少 ? A) 33 B) 39 C) 41 D) 44 ?????????????????????????????????????????????????????????????????????????????? 解答： 設 x 為第 15 個連續整數，而這 29 個連續整數分別為 (x - 14), (x - 13), (x - 12), (x - 11), (x - 10), (x - 9), (x - 8), (x - 7), (x - 6), (x - 5), (x - 4), (x - 3), (x - 2), (x - 1), x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5), (x + 6), (x + 7), (x + 8), (x + 9), (x + 10), (x + 11), (x + 12), (x + 13), (x + 14) ∵ 29 個連續整數的合是 1537 (x - 14) + (x - 13) + (x - 12) + ... + (x - 2) + (x - 1) + x + (x + 1) + (x + 2) + ... + (x + 12) + (x + 13) + (x + 14) = 1537 x + x + x + ... + x - 14 - 13 - 12 - ... - 2 - 1 + 0 + 1 + 2 + ... + 12 + 13 + 14 = 1537 29x = 1537 x = 1537/29 x = 53 則最小的整數是 53 - 14 = 39 ∴ B) 39 ?????????????????????????????????????????????????????????????????????????????? 螞蟻雄兵 的解答： 3個連續整數的和=3*中間數 5連續整數的和=5*中間數 7連續整數的和=7*中間數 … 29連續整數的和=29*中間數 (29+1)/2=15 a15=a1+14*1=14+a1 (14+a1)*29=1537 14+a1=53 a1=39
設最小的數為A[A]=A+A+1+A+3+...+A+28[A]=29A+1+...+28[A]=29A+4061537=29A+4061131=29AA=39答:(B)
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