Class 10

Math

All topics

Arithmetic Progressions

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?

$1,2,3,4,5………………..12$

First term, $a=1$

Common difference, $d=2−1=1$

$S_{n}=2n [2a+(n−1)d]$

$S_{12}=212 [2(1)+(12−1)(1)]$

$=6(2+11)$

$=6(13)$

$=78$

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

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

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