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题库 / OG2017Q-PS-79
A certain drive-in movie theater has a total of 17 rows of parking spaces. There are 20 parking spaces in the first row and 21 parking spaces in the second row. In each subsequent row there are 2 more parking spaces than in the previous row. What is the total number of parking spaces in the movie theater?
412
544
596
632
692
题目分析：
等差数列求和，从第二排开始到第 17 排形成了一个公差为 2 的等差数列， ~$S=n(a_1+a_n)=na_1 + 1/2n n − 1 d$~;
二排到 17 排的和 n=17-2+1=16,d=2, ~$a_1$~=21; S=16*21+1/2*16*15*2=576;
再加上第一排，576+20=596.
综上：答案就是 C
通项公式为：an=a1+(n-1)*d。首项a1=21，公差d=2。前n项和公式为：Sn=a1*n+[n*(n-1)*d]/2或Sn=[n*(a1+an)]/2。注意：以上n均属于正整数。
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