In the following sequence of numbers based on perfect squares, identify which one term is wrong and does not fit the pattern: 49, 36, 25, 18, 9, 4.

Introduction / Context:
This problem asks you to find the wrong term in a series that is otherwise built from perfect squares. Detecting the odd term out in number series requires you to recognize a common mathematical pattern that most terms follow and then identify which number breaks that rule. This is a typical reasoning question in many examinations.

Given Data / Assumptions:
The series is:
49, 36, 25, 18, 9, 4
We assume that the designer of the question intended a consistent mathematical pattern and that exactly one term has been altered or misprinted. Our goal is to find that inconsistent term.

Concept / Approach:
The key idea here is perfect squares of integers in descending order. Perfect squares are numbers of the form n^2. Looking at the sequence, several terms obviously match well known squares: 49 = 7^2, 36 = 6^2, 25 = 5^2, 9 = 3^2, and 4 = 2^2. We should check whether all terms can be expressed as consecutive squares, and if one number cannot, that number is the wrong term.

Step-by-Step Solution:
Step 1: Rewrite each term as a square where possible.49 = 7^236 = 6^225 = 5^29 = 3^24 = 2^2Step 2: Observe the pattern. The squares correspond to descending integers: 7, 6, 5, (4 should appear here), 3, 2.Step 3: The correct descending sequence of squares should be 49, 36, 25, 16, 9, 4.Step 4: Notice that 18 appears where 16 (which is 4^2) should be. Therefore, 18 does not follow the square pattern.

Verification / Alternative check:
Check the differences between consecutive squares. For 7^2 to 6^2, 49 - 36 = 13; 36 - 25 = 11; 25 - 16 = 9; 16 - 9 = 7; 9 - 4 = 5. These are consecutive odd numbers in reverse order. If we compare 25 and 18, 25 - 18 = 7, which does not align with the expected difference of 9. This confirms that 18 breaks the established pattern.

Why Other Options Are Wrong:
49, 36, 25, 9, and 4 are all perfect squares of consecutive integers 7, 6, 5, 3, and 2. They form a consistent descending sequence when combined with the missing 4^2. Therefore, these numbers follow the intended pattern and cannot be the wrong term.

Common Pitfalls:
Some learners may check only whether numbers are perfect squares without considering whether they are in consecutive order. Others might focus on differences between terms and get confused by non constant gaps. The robust method is to map each number to its square root and see if this sequence of roots is consistent and consecutive.

Final Answer:
The only term that does not fit the descending series of perfect squares is 18.