Quite complex algebra problem

Algebra Level 4

$(1 + i) + (3 + 2i) + (5 + 3i) + \ldots + (x + yi)$

The above shows a sum of an arithmetic progression with first term $1+i$ and a common difference $2 + i$ , where $i = \sqrt{-1}$ .

The final term of this sum is $x + yi$ for real numbers $x$ and $y$ .

If this sum is equal to $2500 + 1275i$ , submit your answer as $x+y$ .