Are $-\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.

Are $3, 3+\sqrt{2}, 3+2\sqrt{2}, 3+3\sqrt{2}, \ldots$ in $AP$? If they form an $AP$,find the common difference $d$ and write the next three terms.

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?

Find the sum of the following $APs$ $-37, -33, -29, \ldots$ to $12$ terms.

Find the number of terms in the following $AP$: $7, 13, 19, \ldots, 205$.

The taxi fare after each $km$ when the fare is ₹ $15$ for the first $km$ and ₹ $8$ for each additional $km$. Does the list of numbers involved form an arithmetic progression,and why?