In an A.P., the sum of first n terms is

In an A.P., the sum of first $n$ terms is $\frac{3 n^{2}}{2}+\frac{13}{n} n$. Find its $25^{\text {th }}$ term.


Here, the sum of first n terms is given by the expression,

$S_{n}=\frac{3 n^{2}}{2}+\frac{13}{2} n$

We need to find the 25th term of the A.P.

So we know that the nthterm of an A.P. is given by,


So $a_{25}=S_{25}-S_{24} \ldots \ldots$ (1)

So, using the expression given for the sum of n terms, we find the sum of 25 terms (S25) and the sum of 24 terms (S24). We get,












Now, using the above values in (1),





Therefore, $a_{25}=80$.


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