If the ${\mathrm{m}}^{\text{th }}$ term of an $\mathrm{AP}$ be $\frac{1}{\mathrm{n}}$ and the ${\mathrm{n}}^{\text{th }}$ term be $\frac{1}{ \mathrm{m}}$, then show that the $(\mathrm{mn}{)}^{\mathrm{th}}$ term is $1$.

Find the sum of the following AP:

$40, 36, 32, 28,.....$ to $15$ terms

Find the sum of the following AP:

$3, 8, 13, 18,.....$ to $12$ terms

Find the sum of the following AP:

$-2, -\frac{3}{2}. -1, -\frac{1}{2},.....$ to $25$ terms

Find the sum of the following AP:

$4.5, 4.3, 4.1, 3.9, .....$ to $14$ terms

Find the sum of all terms of the following finite AP:

$63, 61, 59, ....., 35$