In the following number series with one term missing, choose the correct alternative that will complete the series: 41, 43, 47, 53, ?

Introduction / Context:
This verbal reasoning question tests your ability to analyse a simple number series and identify the underlying pattern in the differences between consecutive terms. Such problems appear frequently in banking, SSC and other competitive examinations to measure basic numerical pattern recognition skills.

Given Data / Assumptions:

- The given number series is 41, 43, 47, 53, ?.- Exactly one term is missing, and it must be chosen from the options.- The pattern is assumed to be consistent through the entire series.

Concept / Approach:
The standard approach is to compute the differences between consecutive numbers. In many aptitude questions, these differences themselves form a simple arithmetic sequence or a predictable pattern. Once the pattern in the differences is identified, we extend it to find the missing term. This is often faster and more reliable than trying to see the pattern in the original numbers directly.

Step-by-Step Solution:
Step 1: Find the difference between the second and first terms: 43 - 41 = 2.Step 2: Find the difference between the third and second terms: 47 - 43 = 4.Step 3: Find the difference between the fourth and third terms: 53 - 47 = 6.Step 4: The differences are 2, 4 and 6, which form an increasing pattern where each difference increases by 2.Step 5: Following this rule, the next difference should be 6 + 2 = 8.Step 6: Add this next difference to the last known term: 53 + 8 = 61.Step 7: Therefore the missing term that completes the series is 61.

Verification / Alternative check:
Write the completed series as 41, 43, 47, 53, 61. Now recompute all gaps: 43 - 41 = 2, 47 - 43 = 4, 53 - 47 = 6 and 61 - 53 = 8. The differences are 2, 4, 6, 8, which clearly form an arithmetic progression with common difference 2. Since the rule holds across the entire sequence, the value 61 is fully consistent.

Why Other Options Are Wrong:
If we choose 59, the last difference becomes 59 - 53 = 6, breaking the increasing pattern. If we choose 63 or 65, the last difference becomes 10 or 12, which jumps too far and does not fit the smooth progression of differences 2, 4, 6, 8. Hence these options do not preserve a single simple rule for all the terms in the series.

Common Pitfalls:
Many students guess based on the rough size of the numbers or check only one or two gaps and then stop. Another common mistake is to try complicated operations like squares or cubes before checking simple differences. In exam conditions, always start with the most basic idea: look at the consecutive differences and see if they themselves follow an easy pattern.

Final Answer:
The missing term that correctly completes the series is 61.