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Home » Unlock the Legendary Secret of Kingdom TV Series—Relationships, Betrayals, and More! - inBeat

Unlock the Legendary Secret of Kingdom TV Series—Relationships, Betrayals, and More! - inBeat

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Solution: Set $ -3x + 18 = 4x - 2 $. Solve: $ 18 + 2 = 7x \Rightarrow x = rac{20}{7} $. Substitute into $ y = -3 \cdot rac{20}{7} + 18 = -rac{60}{7} + rac{126}{7} = rac{66}{7} $. Intersection at $ \left( rac{20}{7}, rac{66}{7}

📌 oxed{\left( \dfrac{20}{7}, \dfrac{66}{7}

📌 $$Question: A statistician models a time series using a geometric sequence where the first term is $ 3 $ and the common ratio is $ r $. If the sum of the first five terms exceeds $ 300 $, what is the smallest integer value of $ r $ that satisfies this condition?

📌 The sum of the first five terms of a geometric sequence with first term $ a = 3 $ and common ratio $ r $ is given by:

📌 S_5 = 3(1 + r + r^2 + r^3 + r^4) = 3 \cdot rac{r^5 - 1}{r - 1} \quad ext{(for } r

📌 e 1 ext{)}

📌 \cdot rac{r^5 - 1}{r - 1} > 300

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