Question

In a school, students thought of planting saplings in and around the school to reduce air pollution. It was decided that the number of saplings, 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 two saplings and so on till Class XII. There are three sections of each class. How many saplings will be planted by the students?

• A. 123
• B. 245
• C. 234
• D. 300

Answer 1

The correct option is C

234

There are three sections of each class and it is given that the number of saplings planted by any section of a class is equal to the class number.

The number of saplings planted by class I = number of sections $\times$ 1 = 3 $\times$ 1 = 3

The number of saplings planted by class II = number of sections $\times$ 2 = 3 $\times$ 2 = 6

The number of saplings planted by class III = number of sections $\times$ 3 = 3 $\times$ 3 = 9

Therefore, we have sequence of the form 3, 6, 9, .... 12 terms

To find total number of saplings planted by all the students, we need to find sum of the sequence 3, 6, 9, 12, ... 12 terms.

First term $=a=3$

Common difference $=d=6-3=3$

$n=12$

Applying formula, $S_n=\frac{n}{2}(2a+(n-1\left)d\right)$ to find sum of n terms of AP, we get

$S_{12}=\frac{12}{2}(6+(12-1\left)\right(3\left)\right)$
$=6(6+33)=6\times 39$
$=234$

$\therefore$ Total number of saplings will be planted by the students = 234