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"You Won’t Believe Who’s Secretly the Grimest Danganronpa Character! - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 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 \( a = 3 \), \( d = 2 \), and \( S_n = 110 \), find \( n \).

📌 Substitute into the formula: \( \frac{n}{2}(2 \times 3 + (n-1) \times 2) = 110 \).

📌 Simplify: \( \frac{n}{2}(6 + 2n - 2) = 110 \).

📌 Further simplify: \( \frac{n}{2}(4 + 2n) = 110 \).

📌 Multiply through by 2: \( n(4 + 2n) = 220 \).

📌 Expand: \( 2n^2 + 4n = 220 \).

📌 Rearrange: \( 2n^2 + 4n - 220 = 0 \).

📌 Divide by 2: \( n^2 + 2n - 110 = 0 \).

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