The sum of even numbers between 2 and 50 (inclusive) through average is equal the average of numbers times the number of elements
\(\frac{50+2}{2} * \frac{50-2}{2} +1\)
The same with the sum between 102 and 150
\(\frac{150+102}{2} * \frac{150-102}{2}+1\)
Therefore, we have: the difference of the lager sum and the smaller sum
\((126 * 25) - (26*25) = 25* (126-26) = 25*100= 2500\)
...
\(\frac{50+2}{2} * \frac{50-2}{2} +1\)
The same with the sum between 102 and 150
\(\frac{150+102}{2} * \frac{150-102}{2}+1\)
Therefore, we have: the difference of the lager sum and the smaller sum
\((126 * 25) - (26*25) = 25* (126-26) = 25*100= 2500\)
...
