If the sum of $n$ terms of an $A . P$ . is $3 n^{2} + 5 n$ , then which of its term is $164$

26 t h

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27 t h

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28 t h

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N o n e o f t h e s e

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Solution

The correct option is B $27 t h$
Given, $S_{n} = 3 n^{2} + 5 n$

$S_{1} = 3 + 5 = 8 = a$

$S_{2} = 3 (2)^{2} + 5 (2) = 22 = a_{1} + a_{2}$

$\Rightarrow 8 + a_{2} = 22$

$\Rightarrow a_{2} = 14$

$d = a_{2} - a_{1} = 14 - 8 = 6$

Let $a_{n} = 164$

$\Rightarrow a + (n - 1) d = 164$

$\Rightarrow 8 + (n - 1) 6 = 164$

$\Rightarrow 8 + 6 n - 6 = 164$

$\Rightarrow 6 n = 162$

$\Rightarrow n = 27$

$∴ 27^{t h}$ term is $164$

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