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 students. Which value is shown in the question? [CBSE 2014]

Answer 1

Number of trees planted by the students of each section of class 1 = 2

There are two sections of class 1.

∴ Number of trees planted by the students of class 1 = 2 × 2 = 4

Number of trees planted by the students of each section of class 2 = 4

There are two sections of class 2.

∴ Number of trees planted by the students of class 2 = 2 × 4 = 8

Similarly,

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

So, the number of trees planted by the students of differents classes are 4, 8, 12, ... .

∴ Total number of trees planted by the students = 4 + 8 + 12 + ... up to 12 terms

This series is an arithmetic series.

Here, a = 4, d = 8 − 4 = 4 and n = 12

Using the formula, $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$, we get

$$\begin{gathered} S_{12}=\frac{12}{2}\left[2\times 4+\left(12-1\right)\times 4\right] \\ =6\times \left(8+44\right) \\ =6\times 52 \\ =312 \end{gathered}$$

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

The values shown in the question are social responsibility and awareness for conserving nature.