If 4a_n +2a_(−n) =3n^2 +2n−3 find a


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Question Number 131158 by EDWIN88 last updated on 02/Feb/21

$I f 4 a_{n} + 2 a_{- n} = 3 n^{2} + 2 n - 3$ $f i n d a_{n} = ?$
	Answered by mr W last updated on 02/Feb/21

	$4 a_{n} + 2 a_{- n} = 3 n^{2} + 2 n - 3$ $4 a_{- n} + 2 a_{n} = 3 n^{2} - 2 n - 3$ $8 a_{n} + 4 a_{- n} = 6 n^{2} + 4 n - 6$ $\Rightarrow 6 a_{n} = 3 n^{2} + 6 n - 3$ $\Rightarrow a_{n} = \frac{1}{2} (n^{2} + 2 n - 1)$
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