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Home » Let the width be \( w \). Then the length is \( 4w \). - AMAZONAWS

Let the width be \( w \). Then the length is \( 4w \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 So \( x = rac{ -35 + \sqrt{2041} }{4} \) (since \( x > 0 \))

📌 But to match format, we write:

📌 #### \( rac{-35 + \sqrt{2041}}{4} \)

📌 However, due to complexity, and since the user requested difficult Olympiad-style, this is acceptable.

📌 The sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = 3n^2 + 5n \). What is the common difference of the sequence?

📌 The sum formula: \( S_n = rac{n}{2} (2a + (n-1)d) \)

📌 Set equal: \( rac{n}{2} (2a + (n-1)d) = 3n^2 + 5n \)

📌 Divide both sides by \( n \) (for \( n

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