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?
Solution:
To find the total number of trees planted, let's first tabulate the given information.
Then, we will find the sum using the formula Sₙ = n/2 [2a + (n - 1) d] if they are in AP.
The sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d] or Sₙ = n/2 [a + l], and the nth term of an AP is aₙ = a + (n - 1)d
Here, a is the first term, d is a common difference and n is the number of terms and l is the last term.
| - | Class I | Class II | Class III | … | Class XII |
| Section A | 1 | 2 | 3 | … | 12 |
| Section B | 1 | 2 | 3 | ... | 12 |
| Section C | 1 | 2 | 3 | … | 12 |
| Total | 3 | 6 | 9 | ... | 36 |
It can be observed that the number of trees planted by the students are in an AP.
3, 6, 9, 12, 15,..., 36
- First term, a = 3
- Common difference, d = 6 - 3 = 3
- Number of terms, n =12
We know that sum of n terms of AP,
Sₙ = n/2 [2a + (n - 1) d]
S₁₂ = 12/2 [2 × 3 + (12 - 1) × 3]
= 6 [6 + 11 × 3]
= 6 [6 + 33]
= 6 × 39
= 234
Therefore, 234 trees will be planted by the students
☛ Check: NCERT Solutions Class 10 Maths Chapter 5
Video Solution:
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?
Class 10 Maths NCERT Solutions Chapter 5 Exercise 5.3 Question 17
Summary:
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. If there are three sections of each class, then 234 trees will be planted by the students.
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