16) B

Let difference between r and r + 1 = M

Let difference between r + 1 and r + 2 = N

Let difference between r + 2 and r + 3 = O

The sum of the difference = 126

M + N + O = 126

By understanding the example given in the question, we can infer that:

N = M + 1

O = N + 1

Since N = M + 1,

O = M + 1 + 1 = M + 2

M + N + O = 126

M + M + 1 + M + 2 = 126

3M + 3 = 126

3M = 123

M = 41

M is the difference between r^{th} and (r + 1)^{th} triangular number.

From the example described in the question, we know that:

Difference = initial triangular number + 1.

E.g. Between 2^{nd} triangular number and 3^{rd} triangular number, difference = 3

Initial triangular number is the 2^{nd} triangular number.

Therefore,

M = (r^{th }triangular number) + 1

41 – 1 = r^{th }triangular number

r^{th }triangular number = 40

So the answer is B.