In a school, students thought of planting 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 the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

For Class 1 each section will plant 1 tree and there are 3 sections so total 3 plants will be planted by class 1st.

For Class 2nd each section will plant 2 trees and there are 3 sections so total 6 plants will be planted by class 2nd.

Similarly for class 3rd total trees will be 9.

So,

Total trees = 3 + 6 + 9 + …… + upto 12 terms.

The above list is an A.P. with first term (a) = 3 and common difference = 6 - 3 = 3.

By formula,

Sum upto n terms = S_n = $\dfrac{n}{2}[2a + (n - 1)d]$

Substituting values we get :

$S_{12} = \dfrac{12}{2}[2 \times 3 + (12 - 1) \times 3] \\[1em] = 6[6 + 11 \times 3] \\[1em] = 6 \times [6 + 33] \\[1em] = 6 \times 39 \\[1em] = 234.$

Hence, total trees planted = 234.