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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Perhaps typo in setup? But assume exact: no integer solution.

📌 But wait — perhaps the problem allows approximate? Or we made error.

📌 Alternatively, suppose \( S_n = 210 \), \( n(n+2)=210 \). Try \( n=13 \): 195, \( n=14 \): 224. No integer.

📌 But wait — perhaps the formula: \( S_n = \frac{n}{2}(2a + (n-1)d) = \frac{n}{2}(6 + 2n - 2) = \frac{n}{2}(2n + 4) = n(n + 2) \). Correct.

📌 So no integer \( n \) gives 210? But the problem must have a solution.

📌 Recompute: \( n(n+2) = 210 \), try \( n=13.5 \): \( 13.5 \times 15.5 = 209.25 \), close.

📌 \( n=13.6 \): \( 13.6 \times 15.6 = 211.84 \), too high. So no exact integer.

📌 But in context, likely intended \( n=14 \) with \( S_{14}=224 \), not 210.

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