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 \(x+y\).

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