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?

Options

A. `234`
B. `235`
C. `236`
D. `237`

Answer

To solve the problem of how many trees will be planted by the students in the school, we can follow these steps:

### Step 1: Understand the Problem
Each class from Class I to Class XII will plant a number of trees equal to their class number. For instance, Class I will plant 1 tree, Class II will plant 2 trees, and so on, up to Class XII which will plant 12 trees. There are 3 sections in each class.

### Step 2: Determine the Total Number of Trees Planted by One Class
The number of trees planted by each class can be represented as:
- Class I: 1 tree
- Class II: 2 trees
- Class III: 3 trees
- ...
- Class XII: 12 trees

This forms an arithmetic progression (AP) where:
- First term (a) = 1 (number of trees planted by Class I)
- Last term (l) = 12 (number of trees planted by Class XII)
- Number of terms (n) = 12 (from Class I to Class XII)

### Step 3: Calculate the Sum of Trees Planted by All Classes
The formula for the sum of the first n terms of an arithmetic progression is given by:
\[ S_n = \frac{n}{2} \times (a + l) \]
Where:
- \( S_n \) = sum of the first n terms
- \( n \) = number of terms
- \( a \) = first term
- \( l \) = last term

Substituting the values:
\[ S_{12} = \frac{12}{2} \times (1 + 12) \]
\[ S_{12} = 6 \times 13 \]
\[ S_{12} = 78 \]

So, the total number of trees planted by all classes is 78.

### Step 4: Calculate the Total Number of Trees Planted by All Sections
Since there are 3 sections in each class, the total number of trees planted by all sections is:
\[ \text{Total Trees} = 3 \times S_{12} \]
\[ \text{Total Trees} = 3 \times 78 \]
\[ \text{Total Trees} = 234 \]

### Final Answer
The total number of trees that will be planted by the students is **234 trees**.

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