What will be the nth term of an arithmetic progression if the sum of its $$n$$ term is given by $$2n^2+n$$

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Uniteasy Admin · Accepted Answer

Since the sum of its $$n$$ term is given by $$2n^2+n$$
$$S_n = 2n^2+n$$
$$S_{n-1} =2 (n-1)^2-(n-1)$$
$$a_n = S_n-S_{n-1}$$
$$=2n^2+n-2(n-1)^2-(n-1)$$
$$=2n^2-2(n^2-2n+1)+1$$
$$=4n-1$$

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