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Question
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?
Solution
Since each class has three sections.
Hence, 1 × 3 = 3 trees will be planted by Class I, 2 × 3 = 6 trees by Class II, 3 × 3 = 9 trees by Class III, and similarly, 12 × 3 = 36 trees will be planted by Class XII.
Thus, 3, 6, 9,..., 36 form an AP, where a = 3, d = 6 minus 3 = 3, and n = 12.
1, 2, 3, 4, 5 ... 12
Common difference, d = 2 − 1 = 1
a = 3, d = 6 - 3 = 3, and n = 12
∵ Sn = `"n"/2`[2a + (n - 1) × d]
⇒ S12 = `12/2` [2 × 3 + (12 - 1) × 3]
= 6 [6 + 33]
= 6 × 39
= 234
Thus, the total number of trees is 234.
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