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{1, -3, 4, 1, -3, 4, 1, -3, 4, …}In the sequence above, the first 3 terms repea
{1, -3, 4, 1, -3, 4, 1, -3, 4, …}In the sequence above, the first 3 terms repea
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2024-01-12
31
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问题
{1, -3, 4, 1, -3, 4, 1, -3, 4, …}
In the sequence above, the first 3 terms repeat without end. What is the sum of the terms of the sequence from the 150th term to the 154th term?
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答案
7
解析
由题目可知,这个数列是由1、-3、4三个数字循环组成的数列,若探究之后的某一项是这三个数字中的哪个,则需要用项数除以3,看余数所对应的为哪一项。如看第5项是几,则用5/3=1……2,则说明是三个数中的第2项,是-3,那么第5项也是-3。所以,第150项:150/3=50……0,故第150项为4。按上述规律写出150~154项后可知,上述五项分别为4,1,-3,4,1,求和得7。
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