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📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Only positive root: \( t = 2 + \frac{\sqrt{110}}{5} \approx 2 + 1.05 = 3.05 \) seconds.

📌 Problem:** The sum of the first \( n \) terms of an arithmetic sequence is \( S_n = 3n^2 + 5n \). What is the 10th term?

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

📌 \( a_{10} = S_{10} - S_9 = 350 - 288 = 62 \)

📌 Problem:** A car depreciates such that its value after \( t \) years is \( V(t) = 25000(0.85)^t \). After how many years will its value drop below $10,000?

📌 Solve \( 25000(0.85)^t < 10000 \)

📌 Divide: \( (0.85)^t < \frac{10000}{25000} = 0.4 \)

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