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:
Total class = 12
Section in each class = 3
Number of trees plant by class 1 = 1*3 = 3
Number of trees plant by class 2 = 2*3 = 6
Number of trees plant by class 3 = 3*3 = 9
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Number of trees plant by class 12 = 12*3 = 36
It forms an arithmetic progression
Now
first term a = 3
common difference d = 3
number of terms = 12 (because total number of class = 12)
Now sum of first 12 terms of AP = (n/2) *{2a + (n-1)*d}
= (12/2)*{2*3 + (12-1)*3}
= 6*(6 + 11*3)
= 6*(6 + 33)
= 6*39
= 234
So Number of trees plant by class1 to class12 = 234
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