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 × 1 = 3 × 1 = 3
The number of saplings planted by class II = number of sections × 2 = 3 × 2 = 6
The number of saplings planted by class III = number of sections × 3 = 3 × 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, Sn=n2(2a+(n−1)d) to find sum of n terms of AP, we get
S12=122(6+(12−1)(3))
=6(6+33)=6×39
=234
∴ Total number of saplings will be planted by the students = 234