The sum of the first $n$ terms of an $A P$ is $3 n^{2} + 6 n$ . Find the $n^{t h}$ term of this $A . P .$

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Solution

$\begin{matrix} S u m = 3 x^{2} + n l e t f i r s t t e r m = a c o m m o n d i f f e r e n c e = d s u m = \frac{n}{2} [2 a + (n - 1) d] \frac{2 (3 n^{2} + 6 n)}{n} = 2 a + (n - 1) d 6 n + 12 = 2 a + n d - d x d = 6 n 2 a - d = 12 d = 6 2 a - 6 = 12 = 2 a = 18 = a = 9 a_{n} = a + (n - 1) d a_{n} = 2 + (n - 1) 6 \end{matrix}$

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