Are $1, 3, 9, 27, \ldots$ in $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.

In a potato race,a bucket is placed at the starting point,which is $5\, m$ from the first potato,and the other potatoes are placed $3\, m$ apart in a straight line. There are ten 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 she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run? (in $m$)

In an $AP$ given $a_{n}=4, d=2, S_{n}=-14$,find $n$ and $a$.

For the following $APs$,write the first term and the common difference: $\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, \ldots$

In the following $APs,$ find the missing term in the box: $2, \square, 26$

In a school,students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees,that each section of each class will plant,will be the same as the class,in which they are studying,e.g.,a section of Class $I$ will plant $1$ tree,a section of Class $II$ will plant $2$ trees and so on till Class $XII$. There are three sections of each class. How many trees will be planted by the students?