Canadian Forces Aptitude Test (CFAT) Practice

To determine which fraction follows the sequence, we can analyze the pattern of both the numerators and the denominators.

Looking at the numerators: 1, 6, 15, 28, 45

These numbers are progressive triangular numbers:

- 1 (1st triangular number)

- 6 (3rd triangular number)

- 15 (5th triangular number)

- 28 (7th triangular number)

- 45 (9th triangular number)

The next triangular number in this pattern is the 11th triangular number, which is calculated as \( \frac{11 \times 12}{2} = 66 \).

Now, examining the denominators: 3, 10, 21, 36, 55

These numbers can also be observed as incremental increments, where each is derived from the formula for the triangular numbers:

- 3 (2nd triangular number)

- 10 (4th triangular number)

- 21 (6th triangular number)

- 36 (8th triangular number)

- 55 (10th triangular number)

Following this sequence, the next number in the denominator sequence would be the 12th triangular number, which is calculated as \( \frac{12