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Home » Wake Up—Zealotry Is Destroying Communities Before Your Eyes! - Portal da AcÃºstica

Wake Up—Zealotry Is Destroying Communities Before Your Eyes! - Portal da AcÃºstica

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Final valid attempt:

📌 The sum of the first n terms of an arithmetic sequence is \( S_n = 120 \), with \( a = 4 \), \( d = 4 \). Find n.

📌 \( 120 = \frac{n}{2}(2×4 + (n−1)×4) = \frac{n}{2}(8 + 4n − 4) = \frac{n}{2}(4n + 4) = 2n(n + 1) \)

📌 So \( 2n^2 + 2n = 120 → n^2 + n − 60 = 0 \)

📌 \( n = \frac{-1 \pm \sqrt{1 + 240}}{2} = \frac{-1 \pm \sqrt{241}}{2} \) — not integer.

📌 Try: \( S_n = 90 \), a=5, d=5

📌 \( 90 = \frac{n}{2}(10 + (n−1)5) = \frac{n}{2}(5n + 5) = \frac{5n(n+1)}{2} \)

📌 \( 180 = 5n(n+1) → n(n+1) = 36 → n² + n − 36 = 0 → n = [-1±√145]/2 — not integer.

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