In the following number series, one term is missing. Identify the correct number that completes the pattern: 4, 7, 11, 18, 29, ?

Introduction / Context:
This question presents a number series where each term after the first few is formed by combining information from earlier terms. Such series are slightly more advanced than simple difference based ones because you need to observe relationships between multiple preceding terms rather than only comparing neighbors.

Given Data / Assumptions:
The series is:
4, 7, 11, 18, 29, ?
We assume that the series follows a consistent rule, likely involving sums of previous numbers, and we must extend the series by finding the next term.

Concept / Approach:
The guiding idea is that many series are Fibonacci like, where each term is the sum of the previous two terms. We check if that applies here by testing whether each term from the third term onwards equals the sum of the two terms immediately before it. If this holds for successive terms, we can confidently extend the pattern.

Step-by-Step Solution:
Step 1: Check whether the third term equals the sum of the first two.4 + 7 = 11, which matches the third term.Step 2: Check the fourth term.7 + 11 = 18, which matches the fourth term.Step 3: Check the fifth term.11 + 18 = 29, which matches the fifth term.Step 4: Since the pattern holds, compute the next term as the sum of the previous two terms.18 + 29 = 47.

Verification / Alternative check:
Another way to confirm is to reconstruct the series starting from 4 and 7 while imposing the rule that every new term equals the sum of the previous two. This gives: 4, 7, 11, 18, 29, 47, and so on. No contradictions appear, so 47 is a consistent and unique extension of the series. No other candidate preserves this simple rule of formation.

Why Other Options Are Wrong:
Values such as 45, 30, 32, or 41 do not equal 18 + 29. Choosing any of them would break the established rule that each term after the second is the sum of the preceding two terms. For instance, if we used 45, the sum 18 + 29 would no longer match the next term, and the series would lose its internal consistency.

Common Pitfalls:
Students may mistakenly search for a constant or increasing difference between terms and overlook the possibility that each term is a sum of earlier ones. Another common mistake is arithmetic error in adding the previous two terms. Carefully checking the pattern across several steps avoids such errors.

Final Answer:
The correct number that completes the series is 47.