The sum of $n$ terms of an $A P$ is $3 n^{2} + 5 n$ . Find its $16^{t h}$ term.

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Solution

In $n = 16$
$S_{n} = 3 (16)^{2} + 5 (16)$
$= 768 + 80 = 848$
$S_{15} = 3 (15)^{2} + 5 (15)$
$= 675 + 75 = 750$
$T_{n} = S_{n} - S_{n - 1} = 848 - 750$
$= 98$

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