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.

Given:

The number of trees, that each section of each class will plant, will be double of the class in which they are studying.

There are 1 to 12 classes in the school and each class has two sections.

 To do:

We have to find the number of trees planted by the students.

Solution:

Number of trees planted by each class is as follows:

Class	Sections	Number of trees planted
1	2	$2\times2=4$
2	2	$4\times2=8$
3	2	$6\times2=12$
4	2	$8\times2=16$
5	2	$10\times2=20$
6	2	$12\times2=24$
7	2	$14\times2=28$
8	2	$16\times2=32$
9	2	$18\times2=36$
10	2	$20\times2=40$
11	2	$22\times2=44$
12	2	$24\times2=48$

Total number of trees planted by students of each class is,

$4,8,.....,48$

This is an A.P., where,

$a=4, d=8-4=4$ and $n=12$

We know that,

$S_n=\frac{n}{2}[2a+(n-1)d]$

$=\frac{12}{2}[2(4)+(12-1)4]$

$=6(8+44)$

$=6(52)$

$=312$

Therefore, the total number of trees planted by the students is 312.