I haven't seen this video but the way I think of it is to compare the equation with a chemical balance. Both sides have equal weights and the pointer is at zero. To maintain the pointer at zero if we add/take away a weight from one side we have to do the same thing on the other side.
25 pattern is, 7, 5, and then 3. -2 every time
Be observing the table, we can write the following conjecture:
When adding consecutive even numbers, starting from 2 to

.
Then the sum is equal to:

Then, the sum of the first 15 positive even numbers (which is the sum of 2 to 30) can be calculated with the previous conjecture by setting

:
The answer is 240.
Is a infinite number that keps going