题目信息
The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?
A:10,100
B:10,200
C:15,050
D:20,050
E:20,100
参考答案及共享解析
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已选答案：
正确答案：
E:20,100
Arithmetic Sequences
The sum of the first n positive integers is given by
, so the sum of the first 200 positive integers is 
= 20,100.
Alternatively, letting
represent the sum of the first 100 positive integers, it is given that = 5,050. Using this notation, 
= 
+ 
= + 
+ 
= 
+ 
= 2(5,050) + 10,000
= 10,100 + 10,000 = 20,100.
The correct answer is E.
The sum of the first n positive integers is given by
, so the sum of the first 200 positive integers is = 20,100.Alternatively, letting
represent the sum of the first 100 positive integers, it is given that = 5,050. Using this notation, = + = + + = + = 2(5,050) + 10,000 = 10,100 + 10,000 = 20,100.
The correct answer is E.
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