Let \( a_{n} \) be the \( n^{\text {th }} \) term of an arithmetic progression. Let \( S_{n} \) ...

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Let \( a_{n} \) be the \( n^{\text {th }} \) term of an arithmetic progression. Let \( S_{n} \) be the sum of the first \( n \) terms of the arithmetic progression with \( a_{1}=1 \) and \( a_{3}=3 a_{8} \). Find the largest possible value of \( S_{n} \).
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