In the following number series, exactly one term is wrong. Identify the wrong number: 7.5, 47.5, 87.5, 157.5, 247.5, 357.5, 487.5

Introduction:
This question is a number series puzzle where exactly one term is incorrect. The goal is to detect the underlying pattern that most of the numbers follow and then spot the term that breaks this pattern. Such series questions test observational skills, comfort with differences, and the ability to see second-level patterns in the sequence of differences between consecutive terms.

Given Data / Assumptions:

• Series: 7.5, 47.5, 87.5, 157.5, 247.5, 357.5, 487.5.
• Only one term is wrong.
• All numbers end with .5, suggesting a consistent base increment.

Concept / Approach:
First, compute the differences between consecutive terms to look for a pattern in increments. If the first-level differences are not smooth, examine the second-level differences. Typically, you will find a simple arithmetic pattern (like adding 20 each time) that almost all terms follow, except one. That term is the wrong number.

Step-by-Step Solution:
Compute first-level differences:47.5 - 7.5 = 40.87.5 - 47.5 = 40.157.5 - 87.5 = 70.247.5 - 157.5 = 90.357.5 - 247.5 = 110.487.5 - 357.5 = 130.Now imagine a pattern where the increments increase by 20 each time, starting from 30: 30, 50, 70, 90, 110, 130.Using this ideal pattern from 7.5: 7.5 + 30 = 37.5, 37.5 + 50 = 87.5, 87.5 + 70 = 157.5, 157.5 + 90 = 247.5, 247.5 + 110 = 357.5, 357.5 + 130 = 487.5.So the correct series should be: 7.5, 37.5, 87.5, 157.5, 247.5, 357.5, 487.5.Comparing with the given series, only 47.5 is out of place; it should be 37.5.

Verification / Alternative check:
The corrected differences (30, 50, 70, 90, 110, 130) form a perfect arithmetic pattern with a constant increase of 20. Every term from the third term onwards fits this corrected pattern, confirming that only the second term is wrong.

Why Other Options Are Wrong:
87.5, 247.5, 357.5, 487.5: each of these fits the corrected pattern once the second term is fixed, so they are not wrong.

Common Pitfalls:
Stopping after looking at only first-level differences and not considering how they might ideally progress.Assuming the pattern must be very complex, when a simple increasing-difference pattern works after just one correction.Randomly guessing a term without verifying the full adjusted series.

Final Answer:
47.5