Question

Case Study based-2: In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that each section of each class would plant twice as many plants as the class standard. There were 3 sections of each standard from I to 12. So, if there are three sections in class I say IA. 1B and IC. 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 I to 12 formed an AP given by 6, 12, 18,..

What is the common difference of the AP formed? (a) 6 (b) 5 (c) 2 (d) 3


(II) What will be the nth term of the AP formed? (a) 5n (b) 6n (c) 5n + 6 (d) 6n + 6

(III) How many trees will be planted by the students of all the sections of class 8? (a) 42 (b) 48 (c) 54 (d) 60

(IV) Find the total number of trees planted by class 12 students. (a) 54 (b) 60 (c) 66 (d) None of these

(V) What will be the third term from the end of the AP formed? (a) 72 (b) 66 (c) 60 (d) 54​

Answer 1

Answer:

can be observed that the number of trees planted by the students is in an AP.

1,2,3,4,5………………..12

First term, a=1

Common difference, d=2−1=1

S

n

=

2

n

[2a+(n−1)d]

S

12

=

2

12

[2(1)+(12−1)(1)]

=6(2+11)

=6(13)

=78

Therefore, number of trees planted by 1 section of the classes =78

Number of trees planted by 3 sections of the classes = 3×78=234

Therefore, 234 trees will be planted by the students.