The cost of digging a well after every metre of digging, when it costs ₹ $150$ for the first metre and rises by ₹ $50$ for each subsequent metre, does the list of numbers involved make an arithmetic progression, and why?

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

For the following $APs$,$-5, -1, 3, 7, \ldots$,write the first term and the common difference.

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?

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -2, d = 0.$

For the following $APs,$ $3, 1, -1, -3, \ldots$ write the first term and the common difference.