What is the sum of first n even natural numbers?

The sum of the first n even natural numbers is given by the formula:

Sum = n × (n + 1)

This formula can be derived by recognizing that the sequence of the first n even natural numbers (2, 4, 6, ..., 2n) forms an arithmetic progression (AP) with the first term a = 2 and common difference d = 2.

The sum of the first n terms of an AP is calculated using:

Sum = n/2 × [2a + (n - 1)d]

Substituting the known values:

Sum = n/2 × [2×2 + (n - 1)×2]

Simplifying this expression leads to:

Sum = n × (n + 1)

Therefore, the correct option is:

b. n(n+1)