The sum of first $n$ terms of an A.P. is $3 n^{2} + n$ . Find the $25$ th term of this A.P.

100

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151

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125

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None of these

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Solution

The correct option is B $151$
Given,

$S_{n} = 3 n^{2} + n$

$S_{1} = a_{1} = 3 (1)^{2} + 1 = 4$

$S_{2} = a_{1} + a_{2} = 4 + 3 (2)^{2} + 2 = 18$

$d = a_{2} - a_{1} = 14 - 4 = 10$

$a_{n} = a + (n - 1) d$

$a_{25} = 4 + (25 - 1) 10 = 244$

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