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For positive integers n, if 4a n = (n 2 + 5n + 6) and S n = ∑ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ n 1 k k , a 1 then the value of 507 S 2025 is:

1. 540
2. 1350
3. 675
4. 135

Correct answer: 675

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