Case Study Question 06
Mathematics
Chapter 5: Arithmetic Progressions
Class 10
As a part of this oneweek long festival, students of Durgapura Higher Secondary School thought of planting trees in and around their school to reduce air pollution. It was decided that each section of each class would plant twice as many plants a s class which they belong to. There were 4 sections of each standard from 1 to 12. So, if thereare four sections in class 1 say 1A, 1B , 1C and 1D, then each section would plant 2 trees. Similarly, each section of class 2 would plant 4 trees and so on. Thus, the number of trees planted by classes 1 to 12 formed an AP given by 8, 16, 24, …. Ratan, who is a student of Class 10 B decided to frame a set of questions and answers based on the above information . Help him to do so.
Question.1.
Find the total number of trees planted by class 10 students of all the sections together. Also find the total number of trees planted by students of Ratan’s class alone.
8, 16, 24, ….
To find the total number of trees planted by Class 10 students
of all the 4 sections together, find `a_{10}`.
Here `a= 8`, `d= 8`
`a_{10}= a+9d`
`\Rightarrow a_{10} = 8 + (9 \times 8) = 80` trees
The total number of trees planted by students of Ratan’s class (X B) ` =\frac{80}{4}=20 ` trees.
Question.2.
The members of the Nature Club of the School decided to find the total number of trees planted by the students of the school altogether. Help them to do so.
Sum of trees planted by the students of the school altogether
`S_{n}=\frac{n}{2}[2a+(n1)d]`
`=\frac{12}{2}[2\times8+11\times8]`
`= 624` trees

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