If the nth term of an is $(2 n + 1)$ ,find the sum of the first n terms of the AP.

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Solution

$a_{n} = 2 n + 1$
$a_{1} = 2 + 1 = 3$
$a_{2} = 2 \cdot 2 + 1 = 5$

$d = a_{2} - a_{1}$ $= 5 - 3 = 2$

$S_{n} = \frac{n}{2} [2 a + (n - 1) d]$

$= \frac{n}{2} [6 + (n - 1) 2]$

$= \frac{n}{2} [2 n + 4]$

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