Canadian Forces Aptitude Test (CFAT) Practice

Which fraction follows this sequence: 1/3, 6/10, 15/21, 28/36, 45/55?

1. 81/90

2. 91/105

3. 99/111

4. 66/78

The correct answer is: 91/105

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