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Home » Is Onii Chan Chan the Mysterious Figure Ruining Your Day? Here’s the Truth! - Carbonext

Is Onii Chan Chan the Mysterious Figure Ruining Your Day? Here’s the Truth! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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

📌 Take logarithm: \( t \ln(0.85) < \ln(0.4) \)

📌 \( t > \frac{\ln(0.4)}{\ln(0.85)} \approx \frac{-0.9163}{-0.1625} \approx 5.64 \)

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