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Home » The sum formula for an arithmetic sequence is \( S_n = \fracn2 (2a + (n-1)d) \). - Silent Sales Machine

The sum formula for an arithmetic sequence is \( S_n = \fracn2 (2a + (n-1)d) \). - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \( -5t^2 + 20t + 2 = 0 \)

📌 Use quadratic formula: \( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

📌 \( a = -5, b = 20, c = 2 \)

📌 Discriminant: \( 20^2 - 4(-5)(2) = 400 + 40 = 440 \)

📌 \( t = \frac{-20 \pm \sqrt{440}}{-10} = \frac{-20 \pm 2\sqrt{110}}{-10} = \frac{20 \mp 2\sqrt{110}}{10} = 2 \mp \frac{\sqrt{110}}{5} \)

📌 Only positive root: \( t = 2 + \frac{\sqrt{110}}{5} \approx 2 + 1.05 = 3.05 \) seconds.

📌 Problem:** The sum of the first \( n \) terms of an arithmetic sequence is \( S_n = 3n^2 + 5n \). What is the 10th term?

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