In the following question, select the missing number from the given series: 11, 13, 16, 18, 21, ?

Introduction / Context:
This number series tests the ability to spot a simple alternating pattern in the differences between terms. The sequence 11, 13, 16, 18, 21, ? appears to grow in small steps, suggesting that fixed increments are being added in a repeating cycle. Recognising this cycle quickly is a key skill in reasoning exams.

Given Data / Assumptions:
- Series: 11, 13, 16, 18, 21, ?- Exactly one term, the sixth term, is missing.- All existing terms are positive integers.- The pattern is expected to involve simple additions of small whole numbers.

Concept / Approach:
The standard method is to compute consecutive differences and check whether they repeat. If there is a clear short cycle, such as +2, +3, +2, +3, then we can extend the cycle to find the missing term. We do not need any complex formula; only careful observation of increments is required.

Step-by-Step Solution:
- From 11 to 13: difference = 13 - 11 = 2.- From 13 to 16: difference = 16 - 13 = 3.- From 16 to 18: difference = 18 - 16 = 2.- From 18 to 21: difference = 21 - 18 = 3.- The differences clearly alternate: +2, +3, +2, +3.- The next step should continue this pattern with a difference of +2.- Therefore, the missing term is 21 + 2 = 23.

Verification / Alternative check:
- With the missing term as 23, the full difference sequence becomes 2, 3, 2, 3, 2.- The alternating pattern +2, +3 repeats perfectly throughout the series.- No other candidate produces such a clean and consistent alternation of differences.

Why Other Options Are Wrong:
- 25, 27, 29 and 31 lead to differences that disrupt the neat repeating cycle of +2 and +3.- For example, choosing 25 would add a difference of +4 at the end, which does not match the established pattern.

Common Pitfalls:
- Candidates sometimes miscalculate small differences, especially when working quickly under exam pressure.- It is easy to overthink and search for complex rules when a simple alternating pattern is sufficient.- Ignoring the idea of repetition and treating each difference as unrelated can make the sequence look irregular when it is not.

Final Answer:
The series alternates between adding 2 and adding 3, so the missing term is 23.