The sum of first $q$ terms of an $AP$ is $(63q-3q^2)$. If its $p^{th}$ term is $-60$, find the value of $p$. Also, find the ${11}^{th}$ term of its $AP$.

Find the number of terms of the $AP -12, -9, -6, .........., 21$. If $1$ is added to each term of this $AP$ then the sum of all terms of the $AP$ thus obtained.

Sum of the first $14$ terms of and $AP$ is $1505$ and its first term is $10$. Find its ${25}^{th}$term.

Find the sum of first $51$ terms of an $AP$ whose second and third terms are$14$ and $18$ respectively.

In a potato race, a bucket is placed at the starting point, which is $5 \mathrm{m}$ from the first potato, and the other potatoes are placed $3 \mathrm{m}$ apart in a straight line. There are $10$ potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and he continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

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?