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Home » Shaded area \(= 100 - 25\pi\). - Blask

Shaded area \(= 100 - 25\pi\). - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A sequence is defined recursively by \( a_1 = 2 \), \( a_{2} = 3 \), and \( a_{n} = a_{n-1} + 2a_{n-2} \) for \( n \ge 3 \). Find \( a_6 \).

📌 \( a_3 = a_2 + 2a_1 = 3 + 2(2) = 7 \)

📌 \( a_4 = a_3 + 2a_2 = 7 + 2(3) = 13 \)

📌 \( a_5 = a_4 + 2a_3 = 13 + 2(7) = 27 \)

📌 \( a_6 = a_5 + 2a_4 = 27 + 2(13) = 53 \)

📌 The area of a regular hexagon is \( 54\sqrt{3} \) square units. Find the length of one side.

📌 Area of regular hexagon \( = rac{3\sqrt{3}}{2} s^2 \), where \( s \) is side length.

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