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Home » Summer’s Best Moments: Inspiring Quotes to Feel That Hot Nostalgia Today! - Simpleprint

Summer’s Best Moments: Inspiring Quotes to Feel That Hot Nostalgia Today! - Simpleprint

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 The sum of all four terms is:

📌 The square of the sum is $ (4a)^2 = 16a^2 $.

📌 2a^2 + \frac{9d^2}{2} = 16a^2

📌 \Rightarrow \frac{9d^2}{2} = 14a^2

📌 \Rightarrow d^2 = \frac{28a^2}{9}.

📌 The third term is $ a + \frac{d}{2} $, and the first term is $ a - \frac{3d}{2} $. We want the ratio:

📌 \frac{\text{third term}}{\text{first term}} = \frac{a + \frac{d}{2}}{a - \frac{3d}{2}}.

📌 Substitute $ d^2 = \frac{28a^2}{9} \Rightarrow d = a\sqrt{\frac{28}{9}} = \frac{2a\sqrt{7}}{3} $. Then:

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