# 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:**

To find the total number of trees planted, let's first tabulate the given information.

Then, we will find the sum using the formula Sₙ = n/2 [2a + (n - 1) d] if they are in AP.

The sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d] or Sₙ = n/2 [a + l], and the nth term of an AP is aₙ = a + (n - 1)d

Here, a is the first term, d is a common difference and n is the number of terms and l is the last term.

- | Class I | Class II | Class III | … | Class XII |

Section A | 1 | 2 | 3 | … | 12 |

Section B | 1 | 2 | 3 | ... | 12 |

Section C | 1 | 2 | 3 | … | 12 |

Total | 3 | 6 | 9 | ... | 36 |

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

3, 6, 9, 12, 15,..., 36

- First term, a = 3
- Common difference, d = 6 - 3 = 3
- Number of terms, n =12

We know that sum of n terms of AP,

Sₙ = n/2 [2a + (n - 1) d]

S₁₂ = 12/2 [2 × 3 + (12 - 1) × 3]

= 6 [6 + 11 × 3]

= 6 [6 + 33]

= 6 × 39

= 234

Therefore, 234 trees will be planted by the students

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 5

**Video Solution:**

## 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?

Class 10 Maths NCERT Solutions Chapter 5 Exercise 5.3 Question 17

**Summary:**

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. If there are three sections of each class, then 234 trees will be planted by the students.

**☛ Related Questions:**

- A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, . . .as shown in Fig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? [Take π = 22/7]
- 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on (see Fig. 5.5). In how many rows are the 200 logs placed and how many logs are in the top row?
- In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 × (5 + 3)]

visual curriculum