Which number will complete the series? 11, 13, 17, 19, 23, 25, _____

Introduction / Context:
This series question relies on a simple pattern of alternating increments. The numbers 11, 13, 17, 19, 23, 25, _____ increase by 2 and 4 in turn. Candidates must detect this pattern and extend it by one more step to find the missing term.

Given Data / Assumptions:
- Terms: 11, 13, 17, 19, 23, 25, ?- One final term is missing.- All values are positive integers.- The increments between terms appear to alternate between two fixed small numbers.

Concept / Approach:
The standard technique is to compute consecutive differences and observe any repeating cycle. If we see a pattern like +2, +4, +2, +4, then we know the next difference must continue this cycle. That difference is then added to the last known term to obtain the missing number.

Step-by-Step Solution:
- Difference from 11 to 13: 13 - 11 = 2.- Difference from 13 to 17: 17 - 13 = 4.- Difference from 17 to 19: 19 - 17 = 2.- Difference from 19 to 23: 23 - 19 = 4.- Difference from 23 to 25: 25 - 23 = 2.- The pattern is a repeating cycle of +2, +4, +2, +4, +2.- Therefore, the next difference should be +4.- Add this to the last term: 25 + 4 = 29.- Thus, the missing term is 29.

Verification / Alternative check:
- With 29 included, the complete difference list is 2, 4, 2, 4, 2, 4.- This perfectly preserves the alternating increment pattern throughout the series.- No other candidate value allows this clean repetition.

Why Other Options Are Wrong:
- 25 is already present and would not be a new term in the series.- 27 and 31 correspond to differences of 2 and 6 from 25, breaking the established cycle of +4 after +2.- 33 would lead to an increment of 8, which also does not fit the pattern.

Common Pitfalls:
- Some candidates may notice that many of the numbers are prime and assume a prime pattern, but 25 is not prime, so this is not the correct basis.- Failing to compute all differences accurately may hide the alternating nature of the increments.- Guessing based on the idea of the next prime number, for example 29 or 31, without verifying the difference pattern can lead to partial reasoning instead of complete justification.

Final Answer:
The series alternates between adding 2 and adding 4, so the missing term is 29.