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

It can be observed that the number of trees planted by the students is in an AP.

$1,2,3,4,5\dots \dots \dots \dots \dots \dots ..12$

First term, $a=1$

Common difference, $d=2-1=1$

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$S_{12}=\frac{12}{2}\left[2\right(1)+(12-1\left)\right(1\left)\right]$

$=6(2+11)$

$=6\left(13\right)$

$=78$

Therefore, number of trees planted by $1$ section of the classes $=78$

Number of trees planted by $3$ sections of the classes $=$ $3\times 78=234$

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