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Home » The possible combinations for \((r, d, t)\) are: - AMAZONAWS

The possible combinations for \((r, d, t)\) are: - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 Use Heron’s formula.

📌 Semi-perimeter \( s = \frac{7 + 8 + 9}{2} = 12 \)

📌 Area \( A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{12(12 - 7)(12 - 8)(12 - 9)} = \sqrt{12 \times 5 \times 4 \times 3} = \sqrt{720} = 12\sqrt{5} \)

📌 Problem:** A geometric sequence has first term 3 and third term 27. What is the sum of the first 5 terms?

📌 Let common ratio be \( r \).

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

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

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