There are $25$ trees at equal distance of $5 \mathrm{m}$ in a line with a water tank, the distance of the water tank from the nearest tree being $10 \mathrm{m}$. A gardener waters all the trees separately, starting from the water tank and returning back to the water tank after watering each tree to get water for the next. Find the total distance covered by the gardener in order to water all the trees.

A sum of $₹700$ is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is $₹20$ less than its preceding prize, find the value of each prize.

A man saved $₹33000$ in $10$ months. In each month after the first, he saved $₹100$ more than he did in the preceding month. How much did he save in the first month?

A child puts one five-rupee coin of her savings in the piggy bank on the first day. She increases her saving by one five-rupee coin daily. If the piggy bank can hold $190$ coins of five rupees in all, find $k$, if $\mathrm{k}=\frac{\mathrm{total} \mathrm{money} \mathrm{saved} \mathrm{by} \mathrm{child}}{\mathrm{number} \mathrm{of} \mathrm{days} \mathrm{she} \mathrm{can} \mathrm{contribute}}$.

The first three terms of an $AP$ are respectively $(3y–1), (3y+5)$and $(5y+1)$, find the value of $y$ .

If $k, (2k-1)$ and $(2k+1)$ are the three successive terms of an $AP$, find the value of $k$.

If $18, a, (b-3)$are in $AP$, then find the value of $(2a-b)$