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Home » Multiply through by 3 to clear the fraction: - go-checkin.com

Multiply through by 3 to clear the fraction: - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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

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

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