In this number series reasoning question, find the wrong term in the series: 180, 90, 60, 40, 36.

Introduction / Context:
This question asks you to find the wrong term in the series 180, 90, 60, 40, 36. Unlike standard completion problems, here one of the given terms is incorrect relative to an underlying pattern. Identifying that incorrect term is a common type of logical reasoning task in aptitude exams.

Given Data / Assumptions:

• Series: 180, 90, 60, 40, 36
• Exactly one term is wrong.
• The correct series is generated using a simple consistent rule.

Concept / Approach:
When numbers are decreasing and ratios seem irregular, it often helps to consider division by increasing integers or multiplication by fractions. In many exam problems, a clean pattern like multiplying by successive fractions such as 1/2, 2/3, 3/4, 4/5 is used.

Step-by-Step Solution:
Step 1: Consider dividing 180 by 2.180 * (1 / 2) = 90. This matches the second term.Step 2: Apply the fraction 2/3 to 90.90 * (2 / 3) = 60. This matches the third term.Step 3: Continue the pattern using 3/4.60 * (3 / 4) = 45, but the series shows 40 instead of 45.Step 4: If 45 were present, we would next multiply by 4/5.45 * (4 / 5) = 36, which matches the last term.Step 5: This means the correct series should be 180, 90, 60, 45, 36, and the term 40 is the incorrect one.

Verification / Alternative check:
Using the rule a_{n+1} = a_n * (n / (n + 1)) with n starting from 1 gives the fractions 1/2, 2/3, 3/4, 4/5. Applying these to 180 produces 90, 60, 45 and finally 36. This sequence is mathematically smooth and elegant, confirming that 40 disrupts the pattern and is therefore the wrong term.

Why Other Options Are Wrong:
36: Fits perfectly as 45 * 4 / 5 and is therefore consistent with the intended pattern.
60: Obtained correctly from 90 * 2 / 3, so it is not wrong.
90: Correctly obtained from 180 * 1 / 2, so it is also part of the correct series.

Common Pitfalls:
Students sometimes try simple subtraction and see differences of 90, 30, 20 and 4, which appear irregular and confusing. The trick is to look at fractional multipliers rather than mere differences. Another common error is to suspect the first or last term without verifying the pattern across all steps. Always reconstruct the intended logical sequence before selecting the wrong term.

Final Answer:
The wrong term in the given series is 40.