Question

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?

Answer 1

Compute the number of trees planted.

The number of trees planted by one section of all the classes can be given by:

$1+2+3+....+12$

Which is an $A.P$ with the initial term $a$ as $1$ and common difference $d$ as $1$ and the total numbers of term $n$ as $12$.

So, the sum of this $A.P$.

$$\begin{gathered} \Rightarrow S_{12}=\frac{12}{2}\left(2·1+(12-1)1\right) \\ \Rightarrow S_{12}=6\left(2+11\right) \\ \Rightarrow S_{12}=78 \end{gathered}$$

And the total number of trees planted by all sections of all the classes can be given by:

$78·3=234$

Hence, $234$ trees will be planted by the students.