CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.3 Question 17
17. 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 two trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?
There are three sections of each class and it is given that the number of trees planted by any class is equal to class number.
The number of trees planted by class I = number of sections x 1 = 3 x 1 = 3
The number of trees planted by class II = number of sections x 2 = 3 x 2 = 6
The number of trees planted by class III = number of sections x 3 = 3 x 3 = 9
Therefore, we have sequence of the form 3, 6, 9 .... 12 terms
To find total number of trees planted by all the students, we need to find sum of the sequence 3, 6, 9, 12 ... 12 terms.
First term = a = 3
Common difference = d= 6-3 = 3
n = 12
Applying formula, to find sum of n terms of AP , we get