In the following number series, select the missing number that will correctly complete the sequence: 58, 61, 65, 70, ?, 83.

Introduction / Context:
This problem involves an increasing number series in which the differences between consecutive terms are themselves increasing. Recognizing this secondary pattern in the differences is key to solving the question. Such series are very common in competitive exams to assess logical and numerical reasoning skills.

Given Data / Assumptions:
Given series: 58, 61, 65, 70, ?, 83.The term between 70 and 83 is missing.We assume a smooth, consistent pattern in the differences between terms.

Concept / Approach:
We start by calculating the differences between known consecutive terms. If these differences form a clear pattern, such as a simple arithmetic progression, we can predict the next difference and then determine the missing term. Here, the numbers increase modestly, suggesting that the differences may themselves be small and steadily growing integers like 3, 4, 5, and so on.

Step-by-Step Solution:
Step 1: Compute 61 - 58 = 3.Step 2: Compute 65 - 61 = 4.Step 3: Compute 70 - 65 = 5.Step 4: The differences so far are 3, 4, 5, which strongly suggests that the next differences should be 6 and then 7.Step 5: Let the missing term be x. From 70 to x we should add 6, giving x = 70 + 6 = 76.Step 6: Verify the next step: from x to 83 we should add 7. Indeed, 76 + 7 = 83, exactly matching the last given term.

Verification / Alternative check:
Write the full series with the candidate value: 58, 61, 65, 70, 76, 83. The sequence of differences becomes 3, 4, 5, 6, 7, which is a simple and elegant pattern of consecutive integers. This is a typical structure used in exam questions, and the complete series aligns perfectly with it, providing strong confirmation that 76 is correct.

Why Other Options Are Wrong:
Option 77 would give a difference of 7 from 70 to 77, which skips the expected difference of 6 and makes the pattern of differences inconsistent.Option 78 yields differences 70 to 78 = 8 and 78 to 83 = 5, which do not fit the increasing sequence 3, 4, 5, 6, 7.Option 75 provides differences 5 and 8, again failing to form any simple sequence of steadily increasing differences.

Common Pitfalls:
Some learners might try to average neighbouring terms or look for multiplicative relationships, which are not appropriate here. Another pitfall is to miscalculate one of the differences and thus miss the neat pattern of 3, 4, 5, 6, 7. Always compute each difference carefully and check whether the sequence of differences itself follows a recognizable progression.

Final Answer:
The missing number that completes the series is 76.