Find the common difference of an A.P. whose first term is $\displaystyle 8$, the last term is $\displaystyle 65$ and the sum of all its terms is 730.

\[\begin{aligned} & \mathrm{a}=8, l=65 \\ & 730=\frac{n}{2}[8+65] \\ & n=\frac{730 \times 2}{73}=20 \\ & \begin{aligned} \therefore l=\mathrm{a}+19 \mathrm{~d} & \Rightarrow 65=18+19 \mathrm{~d} \\ & \Rightarrow \mathrm{~d}=3 \end{aligned} \end{aligned} \]