2018 Section 2 Question 16

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.