Let's break down the problem and solve it step by step.
Step 1: Understand the problem
The school has 12 classes, labeled 1 to 12.
Each class has two sections.
The number of trees planted by each section is double the class number. For example, if a student is in class 1, they plant 2 trees; if a student is in class 2, they plant 4 trees, and so on.
The total number of trees planted by the students will be the sum of trees planted by all sections in all classes.
Step 2: Calculate the number of trees planted by each section
For each class, the number of trees planted by each section is twice the class number. So, for class 1, each section plants 2 trees; for class 2, each section plants 4 trees; and so on up to class 12.
Since there are 2 sections per class, the total number of trees planted by both sections of a class is:
Class 1: 2 sections × 2 trees = 4 trees
Class 2: 2 sections × 4 trees = 8 trees
Class 3: 2 sections × 6 trees = 12 trees
Class 4: 2 sections × 8 trees = 16 trees
Class 5: 2 sections × 10 trees = 20 trees
Class 6: 2 sections × 12 trees = 24 trees
Class 7: 2 sections × 14 trees = 28 trees
Class 8: 2 sections × 16 trees = 32 trees
Class 9: 2 sections × 18 trees = 36 trees
Class 10: 2 sections × 20 trees = 40 trees
Class 11: 2 sections × 22 trees = 44 trees
Class 12: 2 sections × 24 trees = 48 trees
Step 3: Add up the total number of trees planted
Now, we add the trees planted by each class:
4 + 8 + 12 + 16 + 20 + 24 + 28 + 32 + 36 + 40 + 44 + 48
Step 4: Perform the calculation
The total number of trees planted is:
4 + 8 = 12
12 + 12 = 24
24 + 16 = 40
40 + 20 = 60
60 + 24 = 84
84 + 28 = 112
112 + 32 = 144
144 + 36 = 180
180 + 40 = 220
220 + 44 = 264
264 + 48 = 312
Step 5: Conclusion
The total number of trees planted by the students is 312.
Value Shown in the Question:
This question shows a concept related to multiplication and summation. It also highlights the concept of progression where the number of trees planted in each class increases linearly with the class number. Specifically, it is an application of arithmetic progression, where the common difference between the number of trees planted in consecutive classes is constant.
