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

The number of trees planted by the students follows an arithmetic progression (AP).
\(1, 2, 3, 4, 5, …..,12\)
The first term is \(a = 1\).
The common difference is \(d = 2 − 1 = 1\).
The formula for the sum of an AP is \(S_n = \frac {n}{2}[ 2a + (n-1)d]\).

For 12 terms, the sum is calculated as follows:
\(S_{12} = \frac {12}{2}[ 2(1) + (12-1)1]\)
\(= 6 (2 + 11)\)
\(= 6 (13)\)
\(= 78\)
Thus, one section of the classes planted 78 trees.
For 3 sections, the total number of trees planted is \(3 \times 78 = 234\).

In total, 234 trees will be planted by the students.