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Home » The sum of the first \( n \) positive integers is 210. What is \( n \)? - DNSFLEX

The sum of the first \( n \) positive integers is 210. What is \( n \)? - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 5a + b &= 7.

📌 Substitute \( a = 1 \) back into \( 3a + b = 5 \):

📌 3(1) + b = 5 \implies b = 2.

📌 Substitute \( a = 1 \) and \( b = 2 \) into \( a + b + c = 6 \):

📌 + 2 + c = 6 \implies c = 3.

📌 Thus, the polynomial is \( f(x) = x^2 + 2x + 3 \).

📌 Now, calculate \( f(x+1) \):

📌 f(x+1) = (x+1)^2 + 2(x+1) + 3.

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