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Home » Shake Your Way to Fit—Chief Lactose-Free Protein Shakes That Deliver! - DNSFLEX

Shake Your Way to Fit—Chief Lactose-Free Protein Shakes That Deliver! - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Solution: Let the four terms be $ a - \frac{3d}{2},\ a - \frac{d}{2},\ a + \frac{d}{2},\ a + \frac{3d}{2} $. This ensures the terms are in arithmetic progression with common difference $ d $. The first term is $ a - \frac{3d}{2} $, and the last term is $ a + \frac{3d}{2} $. Their sum of squares is:

📌 \left(a - \frac{3d}{2}\right)^2 + \left(a + \frac{3d}{2}\right)^2 = 2a^2 + 2\left(\frac{9d^2}{4}\right) = 2a^2 + \frac{9d^2}{2}.

📌 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:

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