If the sum of $n$ terms of an A.P. is $2 n + 3 n^{2}$ , find the $r^{t h}$ term.

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Solution

$\Rightarrow S_{1} = 2 (1) + 3 {(1)}^{2} = 5 S_{n} = \frac{n}{2} {2 a + (n - 1) d} S_{n} = \frac{n}{2} {a + a + (n - 1) d} S_{n} = \frac{n}{2} {a + a_{n}} {2 n + 3 n}^{2} = \frac{n}{2} {5 + a_{n}} 4 + 6 n = 5 + a_{n} \Rightarrow a_{n} = 6 n - 1 \Rightarrow a_{r} = 6 r - 1$

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Find the rth term of an A.P, the sum of whose first n terms is $3 n^{2} + 2 n$

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