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This Brown Sauce Is Taking Websites by Storm—Discover It Now! - ECD Germany

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 The sum of the first n terms of an arithmetic sequence is given by \( S_n = \frac{n}{2}(2a + (n-1)d) \). If \( a = 5 \), \( d = 3 \), and \( S_n = 110 \), find n.

📌 \( 110 = \frac{n}{2}(2 \times 5 + (n-1) \times 3) \)

📌 \( 110 = \frac{n}{2}(10 + 3n - 3) \)

📌 \( 110 = \frac{n}{2}(3n + 7) \)

📌 \( 220 = n(3n + 7) \)

📌 \( 3n^2 + 7n - 220 = 0 \)

📌 Solving the quadratic: \( n = \frac{-7 \pm \sqrt{49 + 2640}}{6} = \frac{-7 \pm \sqrt{2689}}{6} \)

📌 \( \sqrt{2689} \approx 51.85 \), so \( n \approx \frac{44.85}{6} \approx 7.475 \) (not integer)

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