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Home » The sum of the first \( n \) positive integers is 210. Find \( n \). - RTA

The sum of the first \( n \) positive integers is 210. Find \( n \). - RTA

📅 May 12, 2026 👤 scraface

May 12, 2026

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📌 Thus, the coefficients are \( p = 1 \), \( q = 1 \), \( r = 1 \), \( s = 0 \).

📌 \(\boxed{p = 1, \, q = 1, \, r = 1, \, s = 0}\)

📌 A biologist is studying a population of beetles whose growth rate follows a cubic function \( f(x) = ax^3 + bx^2 + cx + d \). Observations show \( f(1) = 4 \), \( f(2) = 15 \), \( f(3) = 40 \), and \( f(4) = 85 \). Determine the coefficients \( a \), \( b \), \( c \), and \( d \).

📌 We solve the system from:

📌 \( a + b + c + d = 4 \)

📌 \( 8a + 4b + 2c + d = 15 \)

📌 \( 27a + 9b + 3c + d = 40 \)

📌 \( 64a + 16b + 4c + d = 85 \)

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