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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
國中數學 等差中項
Feb 28th 2015, 02:36

發問者您好:
此問題,在100至1000的正整數中,所有被四除餘一的整數有幾個?
[解]
100/4=25
101/4=25...1(首項)
1000/4=250
999/4=249...3
998/4=249...2
997/4=249...1(末項)
101,105,109,......,997
公差(d)=4
=>由公試an =a1 +(n-1)d

=>997=101+(n-1)4
整理=>997=101+4n-4
=>997=4n+97
=>4n+900
n=225
所以有225個

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