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# 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, eg. 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?

Given:

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, eg. 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.

To do:

We have to find the number of trees planted by the students.

Solution:

Number of trees planted by each class is as follows:

Class | Sections | Number of trees planted |

I | 3 | $3\times1=4$ |

II | 3 | $3\times2=6$ |

III | 3 | $3\times3=9$ |

IV | 3 | $3\times4=12$ |

V | 3 | $3\times5=15$ |

VI | 3 | $3\times6=18$ |

VII | 3 | $3\times7=21$ |

VIII | 3 | $3\times8=24$ |

IX | 3 | $3\times9=27$ |

X | 3 | $3\times10=30$ |

XI | 3 | $3\times11=33$ |

XII | 3 | $3\times12=36$ |

Total number of trees planted by students of each class is,

$3,6,.....,36$

This is an A.P., where,

$a=3, d=6-3=3$ and $n=12$

We know that,

$S_n=\frac{n}{2}[2a+(n-1)d]$

$=\frac{12}{2}[2(3)+(12-1)3]$

$=6(6+33)$

$=6(39)$

$=234$

Therefore, the total number of trees planted by the students is 234.

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