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Hint- Convert the problem statement in the form of a series of $n$ natural numbers and then find the sum of first $n$ natural numbers.

According to the problem statement, every class has three sections.

Number of trees planted from Class ${\text{I}}$\[ = 3 \times 1\] (1 from each section)

Number of trees planted from Class \[{\text{II}}\]\[ = 3 \times 2\] (2 from each section)

Number of trees planted from Class ${\text{III}}$\[ = 3 \times 3\] (3 from each section)

Number of trees planted from Class ${\text{IV}}$\[ = 3 \times 4\] (4 from each section)

And so on up to Class\[{\text{XII}}\]

Number of trees planted from Class \[{\text{XII}}\]\[ = 3 \times 12\] (12 from each section)

Therefore, for the total number of trees planted we will add all the trees planted from all the classes.

Total number of trees planted\[ = 3 \times 1 + 3 \times 2 + 3 \times 3 + 3 \times 4 + ...... + 3 \times 11 + 3 \times 12 = 3\left[ {1 + 2 + 3 + 4 + ..... + 11 + 12} \right]\]

As we know that the sum of first $n$ natural numbers is given by \[{\text{S}} = \dfrac{{n\left( {n + 1} \right)}}{2}\]

Therefore, the sum of the first 12 natural numbers can be computed if we put \[n = 12\] in the above formula.

i.e., \[1 + 2 + 3 + 4 + ..... + 11 + 12 = \dfrac{{12\left( {12 + 1} \right)}}{2} = \dfrac{{12 \times 13}}{2} = 78\]

Total number of trees planted\[ = 3\left[ {1 + 2 + 3 + 4 + ..... + 11 + 12} \right] = 3 \times 78 = 234\]

Therefore, the total number of trees which are planted by the students are 234 trees.

Note- In these types of problems, it is very crucial to interpret the problem statement very carefully and missing any of the minute detail will lead to a wrong answer. If we observe this particular problem carefully, the sum is reduced to an arithmetic progression for which we have used directly the formula of the sum of first $n$ natural numbers because here the common difference is 1 for the series 1,2,3...12.

According to the problem statement, every class has three sections.

Number of trees planted from Class ${\text{I}}$\[ = 3 \times 1\] (1 from each section)

Number of trees planted from Class \[{\text{II}}\]\[ = 3 \times 2\] (2 from each section)

Number of trees planted from Class ${\text{III}}$\[ = 3 \times 3\] (3 from each section)

Number of trees planted from Class ${\text{IV}}$\[ = 3 \times 4\] (4 from each section)

And so on up to Class\[{\text{XII}}\]

Number of trees planted from Class \[{\text{XII}}\]\[ = 3 \times 12\] (12 from each section)

Therefore, for the total number of trees planted we will add all the trees planted from all the classes.

Total number of trees planted\[ = 3 \times 1 + 3 \times 2 + 3 \times 3 + 3 \times 4 + ...... + 3 \times 11 + 3 \times 12 = 3\left[ {1 + 2 + 3 + 4 + ..... + 11 + 12} \right]\]

As we know that the sum of first $n$ natural numbers is given by \[{\text{S}} = \dfrac{{n\left( {n + 1} \right)}}{2}\]

Therefore, the sum of the first 12 natural numbers can be computed if we put \[n = 12\] in the above formula.

i.e., \[1 + 2 + 3 + 4 + ..... + 11 + 12 = \dfrac{{12\left( {12 + 1} \right)}}{2} = \dfrac{{12 \times 13}}{2} = 78\]

Total number of trees planted\[ = 3\left[ {1 + 2 + 3 + 4 + ..... + 11 + 12} \right] = 3 \times 78 = 234\]

Therefore, the total number of trees which are planted by the students are 234 trees.

Note- In these types of problems, it is very crucial to interpret the problem statement very carefully and missing any of the minute detail will lead to a wrong answer. If we observe this particular problem carefully, the sum is reduced to an arithmetic progression for which we have used directly the formula of the sum of first $n$ natural numbers because here the common difference is 1 for the series 1,2,3...12.

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