Find the missing number in the series: 75, 96, 116, 135, 153, ?

Introduction / Context:
This series uses decreasing differences between consecutive terms. The pattern is that the increment reduces by 1 at each step. Reasoning questions often employ such smoothly changing differences because they are easy to see once carefully computed. The series is 75, 96, 116, 135, 153, ?, and we must identify the next number.

Given Data / Assumptions:
- Series: 75, 96, 116, 135, 153, ?- One final term is missing.- All terms are positive integers and increase steadily.- Differences appear to form a simple pattern, probably decreasing by 1 each time.

Concept / Approach:
We calculate the differences between successive terms and then study how those differences change. If they follow an arithmetic progression, such as 21, 20, 19, 18, 17, we can use this to compute the next increment and hence the missing term.

Step-by-Step Solution:
- From 75 to 96: 96 - 75 = 21.- From 96 to 116: 116 - 96 = 20.- From 116 to 135: 135 - 116 = 19.- From 135 to 153: 153 - 135 = 18.- The differences are 21, 20, 19, 18, decreasing by 1 each time.- The next difference should therefore be 17.- Add this to the last term: 153 + 17 = 170.- So the missing term is 170.

Verification / Alternative check:
- With 170 added, the complete difference sequence is 21, 20, 19, 18, 17.- These differences form a neat arithmetic progression with common difference -1.- No other candidate among the options preserves this exact decreasing pattern.

Why Other Options Are Wrong:
- 173, 178 and 175 correspond to differences of 20, 25 and 22 from 153, which do not continue the -1 step in the increments.- 168 would produce a difference of 15, also breaking the regular sequence of 21, 20, 19, 18, 17.

Common Pitfalls:
- Candidates sometimes assume a constant difference without checking all gaps and get confused when they see variation.- Miscomputing any single difference, such as 135 to 153, can obscure the linear decrease by 1.- Guessing based purely on approximate size of the final term without checking the full pattern may lead to incorrect answers.

Final Answer:
The increments decrease by 1 each time (21, 20, 19, 18, 17), so the missing term is 170.