Sum of first n terms of an A.P is $2 n^{2}$ . Find its nth term.

4n - 4

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4n-2

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2n-4

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2n-2

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Solution

The correct option is B
4n-2

In a sequence, we get the sum of n terms by adding $n^{t h}$ term to the sum of (n-1)terms.
We can write this as $S_{n} = S_{n - 1} + t_{n}$
$\Rightarrow t_{n} = S_{n} - S_{(n - 1)}$
$= 2 n^{2} - 2 (n - 1)^{2}$
$= 2 (n^{2} - (n^{2} - 2 n + 1))$
$= 2 (2 n - 1)$
$= 4 n - 2$

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