Find the number that can replace the question mark in the series below: 6,…

Concept

In a fraction sequence, examine the numerator and denominator as two separate number patterns.

If the numerator and denominator each change regularly, write the general term from those two patterns before evaluating the missing position.

Application

1. Write 6 as 6/1. The terms are therefore 6/1, 7/2, 8/3, 9/4, ?, 11/6.

2. The numerators are 6, 7, 8, 9, 10, 11; each increases by 1.

3. The denominators are 1, 2, 3, 4, 5, 6; each also increases by 1.

4. At the fifth position, the numerator is 10 and the denominator is 5, so the missing fraction is 10/5.

Cross-check

For position n, the term is (n + 5)/n. Substituting n = 5 gives 10/5 = 2, and substituting n = 6 gives 11/6, matching the last given term.

Therefore, the missing number is 2.