In the following simple arithmetic number series, choose the missing term that will correctly complete the series: 5, 9, 13, 17, ?, 25.

Introduction / Context:
This is a straightforward arithmetic number series question. You are given several consecutive terms and asked to identify the missing term that maintains the pattern. Such problems are common in aptitude tests because they quickly reveal how comfortable a candidate is with recognising simple numerical progressions.

Given Data / Assumptions:

- The series is 5, 9, 13, 17, ?, 25.- Exactly one term is missing.- The pattern is assumed to be uniform throughout.

Concept / Approach:
For a series where numbers increase smoothly, the first thing to test is whether it is an arithmetic progression, meaning that we add a constant value each time. To check this, we calculate the difference between each pair of consecutive numbers and see if the difference is constant or follows a simple rule.

Step-by-Step Solution:
Step 1: Compute the difference between the second and first terms: 9 - 5 = 4.Step 2: Compute the difference between the third and second terms: 13 - 9 = 4.Step 3: Compute the difference between the fourth and third terms: 17 - 13 = 4.Step 4: Since all differences are equal to 4, the series is an arithmetic progression with common difference 4.Step 5: To get the next term after 17, add the common difference: 17 + 4 = 21.Step 6: Now check consistency with the last given term: 21 + 4 = 25, which matches the series.

Verification / Alternative check:
The completed series becomes 5, 9, 13, 17, 21, 25. All consecutive differences are 4, confirming that the arithmetic progression rule is upheld across the entire sequence. Therefore, 21 fits perfectly and there is no need for a more complicated explanation.

Why Other Options Are Wrong:
Option 27 produces a difference of 10 from 17, which breaks the constant gap of 4. Option 23 creates differences of 6 and 2 near the end, so it does not maintain a steady pattern. Option 19 would reduce the difference between 17 and the missing term to 2, again violating the rule that every step increases by 4. Hence these options cannot be correct.

Common Pitfalls:
A common mistake is to look at the overall range from 5 to 25 and then guess the middle value without checking each step. Another error is to consider complicated operations like multiplication or division when a simple constant addition works perfectly. Always check differences first before trying more complex patterns.

Final Answer:
The missing term that completes the arithmetic series is 21.