This is the question of arithmetic progression chapter and I found out little bit tricky so please help me in solving this question in which we have been given that 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.
Book RS Aggarwal, Class 10, chapter 5C, question no 42.
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
Sn=n/2[a+l],
Sn=12/2[4+48],
Sn=6×52=312,
Hence, the total number of trees planted by the students is 312.