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

Introduction / Context:
This series repeats the same pattern of alternating increments as a previous example. The numbers 11, 13, 16, 18, 21, ? increase in small steps that follow a cycle of adding 2 and then adding 3. The task is to identify the correct continuation of this simple alternation.

Given Data / Assumptions:
- Series: 11, 13, 16, 18, 21, ?- The sixth term is missing.- All terms are positive integers.- Increments appear to switch between two small values.

Concept / Approach:
We compute differences between consecutive terms and look for a repeating cycle. If the pattern is +2, +3, +2, +3 and so on, then we continue that cycle to obtain the missing number. This is a classic example of an alternating difference sequence.

Step-by-Step Solution:
- From 11 to 13: 13 - 11 = 2.- From 13 to 16: 16 - 13 = 3.- From 16 to 18: 18 - 16 = 2.- From 18 to 21: 21 - 18 = 3.- The differences follow the repeating pattern +2, +3, +2, +3.- The next step should again be +2.- Therefore, the missing term is 21 + 2 = 23.

Verification / Alternative check:
- With 23 as the last term, the full list of differences becomes 2, 3, 2, 3, 2.- This matches the established cycle and confirms the consistency of the pattern across the series.- No other option continues the alternating increments correctly.

Why Other Options Are Wrong:
- 25, 27, 29 and 31 correspond to differences of 4, 6, 8 and 10 from 21, which do not match the expected increment of 2.- Using any of these alternatives would break the neat alternating pattern +2, +3.

Common Pitfalls:
- Careless subtraction can cause the pattern to be misread as something more complicated.- Some candidates may truncate the series and look only at a part of it, missing the full cycle of changes.- Overthinking a simple alternation can lead to unnecessary trial and error with the options.

Final Answer:
The series keeps adding 2 and then 3 alternately, so the missing term is 23.