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. Which value is shown in this question?

Answer 1

Class 1 will plant $=2\times 1\times 2=4$ trees

Class 2 will plant $=2\times 2\times 2=8$ trees

Class 3 will plant $=2\times 3\times 2=12$ trees

Class 4 will plant $=2\times 4\times 2=16$ trees

Class 5 will plant $=2\times 5\times 2=20$ trees

Similarly for 12 will plant $=2\times 12\times 2=48$ trees

So, $4,8,12,16,\mathrm{20....48}$ are in A.P.

Here $a=4,n=12,l=48$

We know that $S_n=\frac{n}{2}[a+l]$

$S_n=\frac{12}{2}[4+48]$

$S_n=6\times 52$

$S_n=312$

Hence, $312$ trees planted by the students.