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. Which value is shown in this question?

Answer 1

As the question shows its makes a series so, we can solve it by using the arithmetic progression and we have the numbers 1 to 12 we can use the sum of $n^{th}$ term formula for finding the total numbers of tree planted by the students of school formula using in this question is
Sum of n terms, (${S_n}$) = $\dfrac{n}{2}\left[ {2a + (n - 1)d} \right]$

Complete step-by-step answer:
As the question says there are two section of each class
Number of trees planted by two sections of class = double of the class number $\times$ number of sections
Number of the trees planted by class 1 = 2 $\times$ 2 = 4
Number of the trees planted by class 2 = 4 $\times$ 2 = 8
Number of the trees planted by class 3 = 6 $\times$ 2 = 12
Number of the tree planted by class 12 = 24 $\times$ 2 = 48
So, the number formed a arithmetic progression
AP = 4, 8, 12………..48
The first term in AP is (a) = 4
The difference between the second and the first term in AP is
d = Second term -first term
d = 8-4 = 4
and the $n^{th}$ term is = 48
number of classes, n = 12
So, here we can easily apply the formula of sum of n terms
${S_n}$=$\dfrac{n}{2}\left[ {2a + (n - 1)d} \right]$
Put the values
${S_{12}} = \dfrac{{12}}{2}\left[ {2 \times 4 + (12 - 1)4} \right]$
${S_{12}} = 6\left[ {8 + 11 \times 4} \right]$
${S_{12}} = 6\left[ {8 + 44} \right]$
${S_{12}} = 6\left[ {52} \right]$
Multiply 6 by 52
${S_{12}} = 312$
So, we have the total number of trees planted by the students is 312.

Note: We can solve this question by alternative method as we know that there is one more formula for finding the sum of n terms i.e. ${S_n} = \dfrac{n}{2}\left[ {a + l} \right]$, where l is the last term and we have our last term in the arithmetic progression is 48.
${S_n} = \dfrac{{12}}{2}\left[ {4 + 48} \right]$
${S_n} = 6\left[ {52} \right]$
${S_n} = 312$
Hence, the total number of trees planted by the students is 312.