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Postdocs: 5 Ã 2 = <<5*2=10>>10 - Portal da AcÃºstica

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Mar 01, 2026

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The sum of the first \( n \) terms of an arithmetic sequence is given...
The \( n \)-th term \( a_n \) can be found using:
\[ S_{n-1} = 3(n-1)^2 + 5(n-1) \]
\[ = 3(n^2 - 2n + 1) + 5n - 5 \]
\[ = 3n^2 - 6n + 3 + 5n - 5 \]
\[ = 3n^2 - n - 2 \]
\[ a_n = (3n^2 + 5n) - (3n^2 - n - 2) \]
\[ = 3n^2 + 5n - 3n^2 + n + 2 \]
\[ = 6n + 2 \]
If \( x^2 - 4x - 21 = 0 \), find the values of \( x \).

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