The sum of first $n$ terms of an A.P is $3 n^{2} + 4 n$ . Find the $25 t h$ term of this A.P.

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Solution

Given : $A P_{n} : 3 n^{2} + 4 n$
$A P_{25} t e r m = 3 (25)^{2} + 4 (25) [n = 25]$
$= 1875 + 100$
$= 1975$
$A P_{24} t e r m s = 3 (24)^{2} + 4 (24)$
$= 1824$
$25^{t h} t e r m = A P_{25} t e r m - A P_{24} t e r m$
$= 1975 - 1824$
$= 151$

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