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Home » How a 13-Year-Old Girl Conquered Fame with Her Unbelievable Blog! - Sterling Industries

How a 13-Year-Old Girl Conquered Fame with Her Unbelievable Blog! - Sterling Industries

📅 April 20, 2026 👤 scraface

Apr 20, 2026

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📌 The sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = 3n^2 + 5n \). What is the \( n \)-th term of the sequence?

📌 The \( n \)-th term \( a_n \) can be found using:

📌 \[ S_{n-1} = 3(n-1)^2 + 5(n-1) \]

📌 \[ = 3(n^2 - 2n + 1) + 5n - 5 \]

📌 \[ = 3n^2 - 6n + 3 + 5n - 5 \]

📌 \[ = 3n^2 - n - 2 \]

📌 \[ a_n = (3n^2 + 5n) - (3n^2 - n - 2) \]

📌 \[ = 3n^2 + 5n - 3n^2 + n + 2 \]

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