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Number series — cubes check: find the wrong term among 1, 8, 27, 64, 124, 216, 343

Difficulty: Easy

Correct Answer: 124

Explanation:


Introduction / Context:
Many classic sequences use perfect powers. Here, most terms are perfect cubes n^3. Spot the one number that is not a perfect cube to identify the odd one out.


Given Data / Assumptions:

  • Series: 1, 8, 27, 64, 124, 216, 343
  • One term is incorrect.


Concept / Approach:
Compute small cubes: 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125, 6^3 = 216, 7^3 = 343. Compare with the sequence given.


Step-by-Step Solution:

Match terms: 1 ✓, 8 ✓, 27 ✓, 64 ✓.Next cube is 5^3 = 125, but the list shows 124 ✗.Then: 216 = 6^3 ✓ and 343 = 7^3 ✓.Therefore, 124 is the only non-cube and is the odd term.


Verification / Alternative check:

Replace 124 with 125 and the series becomes a perfect run of consecutive cubes from 1^3 to 7^3.


Why Other Options Are Wrong:

8, 27, 64 are cubes of 2, 3, 4 respectively, so they are consistent.


Common Pitfalls:

Confusing squares with cubes or misremembering that 5^3 is 125, not 124.


Final Answer:
124

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