A number series is given with one term missing. Observe the sequence 19, 28, 39, 52, ?, 84 and choose the correct alternative that completes the series.

Introduction / Context:
This question presents a steadily increasing number series. The given sequence is 19, 28, 39, 52, ?, 84. Our goal is to determine the missing middle term by analysing the pattern of increases between consecutive numbers. Many such series are built using differences that themselves form a simple sequence, often of consecutive odd or even numbers.

Given Data / Assumptions:
Series: 19, 28, 39, 52, ?, 84.
One term is missing between 52 and 84.
The series increases in a non-linear but regular way.
We assume that the differences between terms themselves follow a clear pattern.

Concept / Approach:
We calculate the differences between consecutive known terms to see whether these differences form a recognizable sequence. In many exam problems, differences are consecutive odd numbers or follow a simple arithmetic progression. Once we identify the pattern in the differences, we can apply it to find the missing term and verify the result.

Step-by-Step Solution:
Compute differences between known terms. 28 - 19 = 9. 39 - 28 = 11. 52 - 39 = 13. The differences so far are 9, 11, and 13, which are consecutive odd numbers. So, the next difference should be 15, followed by 17. Add 15 to 52: 52 + 15 = 67. Add 17 to 67: 67 + 17 = 84, which matches the last term in the series. Therefore, the missing term is 67.

Verification / Alternative check:
With the missing term inserted, the full series becomes 19, 28, 39, 52, 67, 84. The differences are 9, 11, 13, 15, 17, which form a perfect sequence of consecutive odd numbers. This type of structure is common in reasoning questions and confirms that the observed pattern is deliberate and correct.

Why Other Options Are Wrong:
Option A: 39 simply repeats a previous term and breaks the smooth upward trend of the series.
Option B: 52 is already part of the series and cannot appear again as the missing term.
Option D: 84 is the last term and not the missing middle term, so it cannot be correct here.
Option E: 71 would require a difference of 19 from 52 and 13 from 71 to 84, which fails to maintain the consistent pattern of consecutive odd differences.

Common Pitfalls:
Candidates might initially look for a direct multiplicative relation or assume a fixed difference. Others may miscalculate one of the differences and miss the simple odd-number sequence. It is always advisable to carefully compute all differences and look for familiar sequences, especially involving consecutive odd or even numbers.

Final Answer:
The number that maintains the consecutive odd differences pattern is 67, so the correct option is 67.