Two $APs$ have the same common difference. The difference between their $100^{th}$ terms is $100$. What is the difference between their $1000^{th}$ 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?

In which of the following situations,does the list of numbers involved make an arithmetic progression,and why? The amount of air present in a cylinder when a vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylinder at a time.

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

In the following $APs,$ find the missing terms in the boxes $5, \square, \square, 9 \frac{1}{2}$

In a flower bed,there are $23$ rose plants in the first row,$21$ in the second,$19$ in the third,and so on. There are $5$ rose plants in the last row. How many rows are there in the flower bed?