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 five times of the class to which the respective section belongs. If there are 1 to 10 classes in the school and each class has three 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 II, class III, …..& class XII are:

Number of trees planted by the students of two sections of class 1 = 2 $\times$ 2= 4
Number of trees planted by the students of two sections of class 2 = 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, …… 48
This series forms an AP.

Here,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 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.