Difference of Sequences

For the sequence 1,-2,3,-4,5,-6,7,\cdots , what is the difference between the mean of the sequence’s first 400 terms and the mean of its first 200 terms?
Source: NCTM Mathematics Teacher February 2008

Solution
If we add the first 400 terms by pairs 1+(-2),3+(-4),5+(-6),\cdots we end up with 200(-1)=-200. The mean of the first 400 terms is -200/400=-1/2.
Likewise, if we add the first 200 terms by pairs, we get 100(-1)=-100. The mean of the first 200 terms is -100/200=-1/2.
The difference between the two means is -1/2-(-1/2)=0.

Answer: 0

 

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About mvtrinh

Retired high school math teacher.
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