Question

In a school, students decided to plant 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 double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.

Answer 1

Let a be the first term and d be the common difference.
We know that, sum of first n terms = S_n = \[\frac{n}{2}\][2a + (n − 1)d]

It can be observed that the number of trees planted by the students forms an A.P.
2, 4, 6, 8, ... , 24

Here, a = 2, d = 2 and n = 12.

\[\therefore S_n = \frac{12}{2}\left[ 2 \times 2 + \left( 12 - 1 \right)2 \right]\]

         = 6(4 + 22)
        = 6(26)
        = 156

Therefore, trees planted by 1 section of all the classes = 156.
Number of trees planted by 2 sections of all the classes = 2 × 156 = 312
Thus, 312 trees ​were planted by the students.