Answer :

Given there are 1 to 12 classes in school and there are two sections of each class.

So, number of trees that are planted by students of class 1, class 2, class 3, …, class 12 are as follows:

Number of trees planted by class 1 = 2 × 2 = 4

Number of trees planted by class 2 = 2 × 4 = 8

Number of trees planted by class 3 = 2 × 6 = 12

Similarly, number of trees planted by class 12 = 2 × 24 = 48

⇒ Number of trees planted by the students of two sections of classes 1 to 12 are 4, 8, 12, …, 48

The above series form an AP.

From the series, we get

First term, a = 4; Common difference, d = 8 – 4 = 4; Last term, l = 48 and number of terms, n = 12

∴ Number of trees planted by the students = sum of 12 terms of derived AP

We know that the sum of the first n terms of an AP is given by

= 6 (52)

= 312

∴ The number of trees planted by the students is 312.

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