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?
\(234\)
Step 1: Understand the pattern.
For each class from I to XII, every section plants trees equal to the class number.
There are 3 sections in each class.
Step 2: Trees planted by one class.
For Class \(n\) (where \(n = 1, 2, \ldots, 12\)):
• Trees per section = \(n\).
• Number of sections = 3.
• Total trees for that class = \(3n\).
Step 3: Total trees for all classes.
Add trees for Classes I to XII:
\[\text{Total trees} = 3 \cdot 1 + 3 \cdot 2 + 3 \cdot 3 + \cdots + 3 \cdot 12\]
Factor out 3:
\[\text{Total trees} = 3(1 + 2 + 3 + \cdots + 12)\]
Step 4: Use sum of first 12 natural numbers.
Sum of first \(n\) natural numbers:
\[1 + 2 + 3 + \cdots + n = \frac{n(n + 1)}{2}\]
Here \(n = 12\):
\[1 + 2 + 3 + \cdots + 12 = \frac{12 \cdot 13}{2} = \frac{156}{2} = 78\]
Step 5: Multiply by 3 for the sections.
\[\text{Total trees} = 3 \times 78 = 234\]
Conclusion: The students will plant a total of 234 trees.