Even number are of the form 2n. The sum of this sequence is the average of the first and last terms times the number of terms.
So the first term is 2 and the 25th term is 50 so the sum is:
(2+50)(25/2)
52*12.5=650
The conjecture they wish you to make is that for n terms, the sum will be:
s=n(n+1)
And for 25 terms that would give you:
s=25*26=650
