The sum of n terms of an AP is $2 n^{2} + n$ . Then 8th term of the A.P is

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Solution

The correct option is A 31
$S_{n} \Rightarrow \frac{n}{2} [2 a + (n - 1) d] = 2 n^{2} + n$
$\frac{2 a + (n - 1) d}{2} = 2 n + 1$
$2 a + (n - 1) d = 4 n + 2$
$\frac{2 a}{2} + (\frac{n - 1}{2}) = 2 n + 1$
$a + (\frac{n - 1}{2}) d = 2 n + 1...... (i)$
$T_{8} = a + 7 d . . . . (i i)$

comparing eq (i) and (ii)

$\frac{n - 1}{2} = 7$
$∴$ $n - 1 = 14$
$n = 15,$

Putting $n = 15$
$a + 7 d = 2 \times 15 + 1$
$= 30 + 1$
$T_{8} = 30$

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