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中五數學 ------ Arithmetic and Geometric Sequences

發問:

1.(a)Find the smallest multiple and the largest multiple of 9 between 300 and 800. (b)Find the sum of all multiples of 9 lying between 300 and 800.2.(a)Find the sum of all multiples of 3 lying between 400 and 500. (b)Find the sum of all multiples of 6 lying between 400 and 500. (c)Between 400 and... 顯示更多 1.(a)Find the smallest multiple and the largest multiple of 9 between 300 and 800. (b)Find the sum of all multiples of 9 lying between 300 and 800. 2.(a)Find the sum of all multiples of 3 lying between 400 and 500. (b)Find the sum of all multiples of 6 lying between 400 and 500. (c)Between 400 and 500,find the sum of all integers that are multiples of 3 but not multiples of 6.

最佳解答:

1(a) smallest=306 largest=792 (b) Let 792 be the n term 306+(n-1)9=792 n=55 ∴sum of all multiples of 9 lying between 300 and 800 =(306+792)(55)÷2 =30195 2(a) smallest=402 largest=498 Let 498 be the n term 402+(n-1)(3)=498 n=33 ∴sum of all multiples of 3 lying between 400 and 500 =(402)(498)(33)÷2 =14850 (b) smallest=402 largest=498 Let 498 be the n term 402+(n-1)(6)=498 n=17 ∴sum of all multiples of 6 lying between 400 and 500 =(402)(498)(17)÷2 =7650 (c) sum of all integers that are multiples of 3 but not multiples of 6 =14850-7650 =7200

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