Q : 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 \small 1 tree, a section of Class II will plant \small 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

Answers (1)

First there are 12 classes and each class has 3 sections
Since each section of class 1 will plant 1 tree, so 3 trees will be planted by 3 sections of class 1.Thus every class will plant 3 times the number of their class 
Similarly,

No. of trees planted by 3 sections of class 1 = 3

No. of trees planted by 3 sections of class 2 = 6

No. of trees planted by 3 sections of class 3 = 9

No. of trees planted by 3 sections of class 4 = 12
Its clearly an AP with first term(a)3 and common difference(d)3 and  total number of classes(n) = 12

Now, number of trees planted by 12 classes is given by
S_{12}= \frac{12}{2}\left \{ 2\times 3+(12-1)\times 3 \right \}
S_{12}= 6\left ( 6+33 \right )
S_{12}= 6 \times 39 = 234
Therefore,  number of trees planted by 12 classes is 234

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