What is the sum of the first 2,003 terms of the sequence 0,2,7,1,0,2,7,1,0,2,7,

游客2024-01-12  16

问题 What is the sum of the first 2,003 terms of the sequence 0,2,7,1,0,2,7,1,0,2,7, 1, ……if the pattern 0,2,7,1 is repeated throughout the sequence?

选项 A、503
B、2010
C、2013
D、5009
E、20030

答案 D

解析 若整个序列O,2,7,1,0,2,7,1,…以0,2,7,1循环,那么该数列前2003项的和是多少?
解:本题的正确答案为(D)。由于数列是以0,2,7,1为周期循环,其周期长度为4,所以前2003项共有2003/4=500个周期,并余3项:O,2,7。因此该数列前2003项的和为:500×(0+2+7+1)+(0+2+7)=5009
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