In this aptitude number series question, find the missing number in the series: 5, 9, 15, 23, ?, 45.

Introduction / Context:
This aptitude question tests understanding of simple number series based on increasing differences. Such questions are common in competitive exams and interview tests where you must quickly identify the underlying pattern and use it to find the missing term in the sequence 5, 9, 15, 23, ?, 45.

Given Data / Assumptions:

• Given series: 5, 9, 15, 23, ?, 45
• Exactly one term is missing in the middle of the series.
• The pattern is assumed to be consistent throughout the sequence.
• Only one option should correctly complete the series.

Concept / Approach:
The most common approach in such series is to look at the differences between consecutive terms. If those differences follow a simple pattern, we can extend that pattern to find the missing number. Often, the differences may themselves form an arithmetic progression or follow a simple incremental rule.

Step-by-Step Solution:
Step 1: Find the differences between consecutive terms.5 to 9: 9 - 5 = 49 to 15: 15 - 9 = 615 to 23: 23 - 15 = 8Step 2: Observe the pattern in the differences: 4, 6, 8.Step 3: The differences are increasing by 2 each time: 4, 6, 8, 10, 12.Step 4: Add the next difference 10 to 23 to get the missing term: 23 + 10 = 33.Step 5: Check the next step: 33 + 12 = 45, which matches the last given term.

Verification / Alternative check:
If the difference pattern is correct, all terms including the last one must fit. Using 33 as the missing term gives differences 4, 6, 8, 10, 12, forming a clean arithmetic progression with common difference 2. This confirms that 33 is consistent with the entire series.

Why Other Options Are Wrong:
29: This would give a difference of 6 from 23 and then 16 to 45, breaking the smooth pattern of increasing differences by 2.
31: This would create differences 4, 6, 8, 8, 14, which do not form any simple regular pattern.
35: This would give differences 4, 6, 8, 12, 10, again destroying the consistent increase by 2 in the differences.

Common Pitfalls:
A common error is to look only at the numbers themselves without examining the differences, or to stop after checking only the first few steps of the pattern. Sometimes students also guess based on rough size rather than a clear numeric rule. Always verify that your chosen number keeps the pattern valid for the entire series, including the last term.

Final Answer:
The missing number that correctly completes the series is 33.