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university of north carolina at pembroke - Decision Point

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 The sum of the first \(n\) terms of an arithmetic sequence is given by \(S_n = 3n^2 + 5n\). Find the 10th term of the sequence.

📌 The \(n\)-th term \(a_n\) is given by \(a_n = S_n - S_{n-1}\).

📌 \(S_{10} = 3(10)^2 + 5(10) = 300 + 50 = 350\).

📌 \(S_9 = 3(9)^2 + 5(9) = 243 + 45 = 288\).

📌 Thus, \(a_{10} = 350 - 288 = 62\).

📌 A train travels 120 km at a speed of \(v\) km/h and then 180 km at \(v + 20\) km/h. If the total time for the journey is 5 hours, find \(v\).

📌 The time for the first part is \(\frac{120}{v}\) hours.

📌 The time for the second part is \(\frac{180}{v+20}\) hours.

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