In the number series 8, 27, 125, 343, 1381, one term is wrong. Identify the number that does not fit the pattern.

Introduction / Context:
The series 8, 27, 125, 343, 1381 clearly suggests powers, especially cubes, because 8, 27, 125 and 343 are well known cube values. The task is to see which term departs from this neat cubic pattern and therefore must be the wrong term.

Given Data / Assumptions:

• Series: 8, 27, 125, 343, 1381.
• Exactly one term is incorrect.
• The correct terms are expected to be cubes of integers, probably prime numbers.

Concept / Approach:
We test each number to see whether it is a perfect cube. If all but one term are cubes of consecutive primes (or integers), that non cube is the wrong term. This is a standard construction used frequently in reasoning and aptitude questions.

Step-by-Step Solution:
1. Test 8: 2^3 = 8, so 8 is a perfect cube. 2. Test 27: 3^3 = 27, so 27 is a perfect cube. 3. Test 125: 5^3 = 125, so 125 is a perfect cube. 4. Test 343: 7^3 = 343, so 343 is a perfect cube. 5. Observe that the bases 2, 3, 5, 7 are consecutive prime numbers. 6. The next prime after 7 is 11, so the next term in this pattern should be 11^3. 7. Compute 11^3: 11 * 11 = 121 and 121 * 11 = 1331. 8. So the last term should be 1331, but the given series has 1381. 9. Therefore, 1381 is the wrong term.

Verification / Alternative check:
Construct the ideal series based on consecutive primes: 2^3 = 8, 3^3 = 27, 5^3 = 125, 7^3 = 343, 11^3 = 1331. The pattern of cube bases is: 2, 3, 5, 7, 11 which are clearly consecutive primes. The given last term 1381 is not equal to 1331 and is not a cube of any integer, so it violates the structure.

Why Other Options Are Wrong:

• 8, 27, 343: Each of these is a perfect cube of a prime (2, 3, 7 respectively) and fits the sequence of prime cubes.

Common Pitfalls:
Sometimes candidates will compute differences between successive terms and get lost in complicated arithmetic. When numbers look like 8, 27, 125 and 343, the first check should always be whether they are perfect cubes or squares. Recognising the prime cube pattern here quickly isolates the outlier.

Final Answer:
The wrong term in the series is 1381.