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標題:

Find the sum of the arithmetic serires!!!

發問:

Find the sum of the arithmetic series a. 100 +102 +104 +....to 20 terms b. 2 +6 +10 +14+...+ 34 請問點做呢?

最佳解答:

a.每項相差2 第20 terms即係 100+2x(20-1)=118 個差一樣...就可以用(頭+尾)x項數/2 100+102 +104+...+118= (100+118)x20/2 =2180 b.2 +6 +10 +14+...+ 34 每個差都一樣..係4 2+4(n-1)=34 4n=34+2 n=9 34係第9項.. 2 +6 +10 +14+...+ 34=(2+34)x9/2 =162

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a) the sum of the arithmetic series = (n/2)x[2a (n-1)d] n=no. of terms n=20 a= first term a=100 d=difference between two terms d=102-100 d=2 the sum of the arithmetic series=(20/2)x[2(100) (19)(2)] =2380 b) the sum of the arithmetic series also = (n/2)x(a l) where l =last term By a), a (n-1)d =l 2 (n-1)(6-2)=34 n=9 the sum of the arithmetic series=(9/2)x(2 34) =162 2008-06-06 00:20:01 補充： 我試過逐個數禁黎CHECK答案，包準!!