NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 17

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 17

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?

Given:

Number of classes = 12
Number of sections per class = 3
Trees planted by each section of class n = n

To Find:

Total number of trees planted by the students.

Formula:

Sum of n terms of AP: Sn = \( \frac{n}{2} \) × (a + l)

Solution:

Let us find the number of trees planted by the 1st section of the students.

Class 1, section 1 = 1 

Class 2, section 1 = 2

Class 12, section 1 = 12

This forms an AP 1, 2, 3, ....., 12

Here, a = 1, l = 12, n = 12

Tthe number of trees planted by the 1st section of the students  is given by the formula Sn = \( \frac{n}{2} \) × (a + l) 

⇒ S12 = \( \frac{12}{2} \) × (1 + 12)

⇒ S12 = 6 × 13 

⇒ S12 = 78

78 trees are planted by one section of each class. 

Since there are three sections in each class, 

The total number of trees planted = 3 × Tress planted by one section of each class 

⇒ Total number of tress planted = 3 x 78 

⇒ Total number of tress planted = 234

Result:

The students will plant a total of 234 trees.

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