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Home » How Nanamacs Changed the Game—Watch Coders Go Wild with This Power Tool! - Simpleprint

How Nanamacs Changed the Game—Watch Coders Go Wild with This Power Tool! - Simpleprint

📅 March 13, 2026 👤 scraface

Mar 13, 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 sum of the first 10 terms is 150 and the first term is 5, what is the common difference \( d \)?

📌 Substitute \( n = 10 \), \( S_{10} = 150 \), \( a = 5 \):

📌 \( 150 = \frac{10}{2}(2 \cdot 5 + 9d) = 5(10 + 9d) \).

📌 So, \( 150 = 50 + 45d \).

📌 Then, \( 100 = 45d \) and \( d = \frac{20}{9} \).

📌 A line passes through the points \( (3, 7) \) and \( (-1, -5) \). What is the slope of a line perpendicular to this line?

📌 The slope of the original line is \( m = \frac{7 - (-5)}{3 - (-1)} = \frac{12}{4} = 3 \).

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