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mole to mole relationship - ECD Germany

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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

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

📌 \( 2a + (n-1)d = 6n + 10 \)

📌 Expand left: \( 2a + dn - d = dn + (2a - d) \)

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