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Sum of N Terms of an AP

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Question

Find the sum of $^{'} n^{'}$ terms of A.P. whose $r t h$ term is $2 r + 3 .$

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Solution

rth term $= 2 r + 3$
Sum $= 2 \sum_{n = 0}^{n} r + \sum_{n = 0}^{n} 3 = 2 \frac{(n) (n + 1)}{2} + 3 n$
$= n^{2} + 4 n$

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