First solution:

Since the integers from 200 to 400, inclusive, are members of an arithmetic progression then the average can be calculated by the formula
The integers from 50 to 100, inclusive, are members of an arithmetic progression as well and the average can be calculated by the formula


Therefore, the average of integers from 200 to 400, inclusive, is greater than the average of integers from 50 to 100, inclusive, by 225.

Useful formulas:

If numbers are members of an arithmetic progression, then there exists a number d for every Then the average of this sequence can be calculated by the formula

For example, if
is an arithmetic progression, then d=2 and its average is 6
The list of integers from 13 to 237 is an arithmetic progression too (d=1) and average is 125