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?

Given there are 1 to 12 classes in school and there are two sections of each class.

So, number of trees that are planted by students of class 1, class 2, class 3, …, class 12 are as follows:

Number of trees planted by class 1 = 2 × 2 = 4

Number of trees planted by class 2 = 2 × 4 = 8

Number of trees planted by class 3 = 2 × 6 = 12

Similarly, number of trees planted by class 12 = 2 × 24 = 48

⇒ Number of trees planted by the students of two sections of classes 1 to 12 are 4, 8, 12, …, 48

The above series form an AP.

From the series, we get

First term, a = 4; Common difference, d = 8 – 4 = 4; Last term, l = 48 and number of terms, n = 12

∴ Number of trees planted by the students = sum of 12 terms of derived AP

We know that the sum of the first n terms of an AP is given by

= 6 (52)

= 312

∴ The number of trees planted by the students is 312.