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Home » Rounded to nearest person: 3002 - Dachbleche24

Rounded to nearest person: 3002 - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 The sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = \frac{n}{2}(2a + (n-1)d) \). If the first term is 5 and the common difference is 3, find \( S_{15} \).

📌 \( a = 5, d = 3, n = 15 \)

📌 \( S_{15} = \frac{15}{2}(2 \times 5 + 14 \times 3) \)

📌 \( S_{15} = \frac{15}{2}(10 + 42) \)

📌 \( S_{15} = \frac{15}{2} \times 52 = 15 \times 26 = 390 \)

📌 A right triangle has legs of lengths \( x \) and \( x+3 \), and a hypotenuse of length \( x+5 \). Find the value of \( x \).

📌 Using Pythagoras: \( x^2 + (x+3)^2 = (x+5)^2 \)

📌 Expand: \( x^2 + x^2 + 6x + 9 = x^2 + 10x + 25 \)

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