In an A.P., the sum of first n terms is $\displaystyle \frac{\mathrm{n}}{2}(3 \mathrm{n}+5)$. Find the $\displaystyle 25{ }^{\text {th }}$ term of the A.P.

\[\begin{aligned} & S_{n}=\frac{3 n^{2}}{2}+\frac{5 n}{2} \\ & n=1, S_{1}=\frac{3}{2}+\frac{5}{2}=4 \rightarrow 1 \text { st term } a_{1} \\ & n=2, S_{2}=\frac{3 \times 4}{2}+\frac{5(2)}{2}=11(1 \text { st term }+ \text { 2nd term }) \\ & \therefore a_{2}=S_{2}-S_{1}=11-4=7 \\ & d=a_{2}-a_{1}=7-4=3 \\ & a_{25}=a+24 d=4+24(3)=76 \end{aligned} \]