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? [CBSE 2014]​

Answer 1

Answer:

Formula I used is:

Sum of n natural numbers is = n(n+1)/2

Step-by-step explanation:

Because each section plants double the amount of trees they are studying in, and each class has 2 sections,

Then total trees planted

= 2×2×1 + 2×2×2 + 2×2×3 + 2×2×4 + 2×2×5.... +2×2×12

= 4( 1+2+3+4+...12)

= 4 × 12×13/2 = 312

Total 312 trees were planted.

Answer 2

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 I=2×2=4
Number of trees planted by the students of two sections of class II=2×4=8
Similarly,
Number of trees planted by the students of two sections of class 3=2×6=12
Number of trees planted by the students of two sections of class12=2×24=48
So, the number of trees planted by the students of two sections of different classes are4,8,12,……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
​
=
2
n
​
[a+l],
S
n
​
=
2
12
​
[4+48],

S
n
​
=6×52=312,

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

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