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Home » A geometric sequence starts with 2 and has a common ratio of 3. What is the 6th term? - Aurero

A geometric sequence starts with 2 and has a common ratio of 3. What is the 6th term? - Aurero

📅 March 16, 2026 👤 scraface

Mar 16, 2026

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ec{OA} \cdot ec{OB} = (-1 + \sqrt{7})(-1 - \sqrt{7}) + (1 + \sqrt{7})...
= [(-1)^2 - (\sqrt{7})^2] + [1 - (\sqrt{7})^2] = (1 - 7) + (1 - 7) = -...
Magnitudes:
|ec{OA}| = \sqrt{(-1 + \sqrt{7})^2 + (1 + \sqrt{7})^2} = \sqrt{(1 - 2...
|ec{OB}| = \sqrt{(-1 - \sqrt{7})^2 + (1 - \sqrt{7})^2} = \sqrt{(1 + 2...
\cos heta = rac{-12}{(2\sqrt{6})(2\sqrt{6})} = rac{-12}{24} = -rac...
The area of the circular sector is:
A_{ ext{sector}} = rac{1}{2} r^2 heta = rac{1}{2} \cdot 16 \cdot r...
Area of triangle \(OAB\):
A_{ ext{triangle}} = rac{1}{2} ab \sin heta = rac{1}{2} (2\sqrt{6})...

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