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Sum of N Terms of an AP

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Question

Find the sum of the series to $n$ terms whose general term is $2 n + 1.$

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Solution

$S_{n} = \sum T_{n} = \sum (2 n + 1)$
$= 2 \sum n + \sum 1$
$= \frac{2 (n + 1) n}{2} + n = n^{2} + 2 n$

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