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

According to the question , there are two sections of each class so the number of trees that are planted by students of class $I$, class $I$I, class $III$, …..& class $XII$ are:

Number of trees planted by the students of two sections of class $I=2\times 2=4$

Number of trees planted by the students of two sections of class $II=2\times 4=8$

Similarly,

Number of trees planted by the students of two sections of class $3=2\times 6=12$

Number of trees planted by the students of two sections of class$12=2\times 24=48$

So, the number of trees planted by the students of two sections of different classes are$4,8,12,\dots \dots 48$

This series forms an AP

Here,first term$\left(a\right)=4$, common Difference $\left(d\right)=8–4=4$, last term $\left(l\right)=48$ and (number of terms)$n=12$

Number of trees planted by the students $=$sum of $12$ terms of above AP

$S_n=\frac{n}{2}[a+l]$,

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

$S_n=6\times 52=312$,

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