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oxed{\left( \dfrac85,\ \dfrac215 - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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Verify: \( S_{14} = \frac{14}{2}(6 + 26) = 7 \times 32 = 224 \) → too...
Try \( n = 13 \): \( S_{13} = \frac{13}{2}(6 + 24) = 6.5 \times 30 = 1...
Recheck equation: \( n(n + 2) = 210 \) → \( n^2 + 2n - 210 = 0 \).
Discriminant: \( 4 + 840 = 844 \), \( \sqrt{844} \approx 29.05 \), so...
Wait: \( n(n+2) = 210 \), try factor pairs: \( 14 \times 15 = 210 \),...
\( 14 \times 16 = 224 \), \( 13 \times 15 = 195 \), no integer solutio...
Actually, solve exactly: \( n = \frac{-2 + \sqrt{4 + 840}}{2} = \frac{...
No integer \( n \) satisfies? But problem implies one.
Re-check: \( S_n = \frac{n}{2}(2a + (n-1)d) = \frac{n}{2}(6 + (n-1)2)...
Discriminant: \( 4 + 840 = 844 \), not a perfect square. But 13.525 no...

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