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Home » a_n = 2 + (n - 1) \times 3 = 3n - 1 - Crosslake

a_n = 2 + (n - 1) \times 3 = 3n - 1 - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Let common ratio be \( r \).

📌 \( a_1 = 3 \), \( a_3 = 3r^2 = 27 \Rightarrow r^2 = 9 \Rightarrow r = 3 \) (assuming positive)

📌 Sum \( S_5 = 3 \frac{3^5 - 1}{3 - 1} = \frac{3(243 - 1)}{2} = \frac{3 \times 242}{2} = 363 \)

📌 Problem:** Solve for \( x \): \( \log_2(x + 3) + \log_2(x - 1) = 3 \).

📌 Combine logs: \( \log_2((x + 3)(x - 1)) = 3 \)

📌 So \( (x + 3)(x - 1) = 2^3 = 8 \)

📌 Expand: \( x^2 + 2x - 3 = 8 \Rightarrow x^2 + 2x - 11 = 0 \)

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