For the sequence , what is the difference between the mean of the sequence’s first terms and the mean of its first terms?

Source: NCTM Mathematics Teacher February 2008

**Solution**

If we add the first terms by pairs we end up with . The mean of the first terms is .

Likewise, if we add the first terms by pairs, we get . The mean of the first terms is .

The difference between the two means is .

**Answer**: