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?
The total number of trees planted by the students will be 234 trees.
Explanation
This question involves finding the sum of an Arithmetic Progression (AP). The number of trees planted by each section follows the pattern: 1, 2, 3, ..., 12 (for Classes I to XII). Since there are 3 sections in each class, we need to multiply the sum of this AP by 3. The sum formula S_n = n/2 × (a + l) is applied where n=12, a=1, and l=12.
Solution Steps
Step 1: Identify the number of trees planted by each section of classes I to XII. The sequence is: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. This forms an Arithmetic Progression (AP) with first term a = 1, last term l = 12, and number of terms n = 12.
Step 2: Calculate the sum of this AP using the formula: S_n = n/2 × (a + l). Substituting the values: S_12 = 12/2 × (1 + 12) = = 78 trees.
Step 3: Since there are 3 sections in each class, multiply the sum by 3 to get the total number of trees. Total trees = = 234 trees.