Show that $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ form an $AP$ where $a_{n}$ is defined as $a_{n}=9-5n$. Find the sum of the first $15$ terms.

Are $\sqrt{3}, \sqrt{6}, \sqrt{9}, \sqrt{12}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more 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?

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 an $AP$,given $a=2, d=8, S_{n}=90$,find $n$ and $a_{n}$.

Which term of the $AP : 3, 8, 13, 18, \ldots$ is $78$ (in $^{th}$)?