Number series (perfect cubes): 1, 8, 27, 64, 125, 216, (…) Identify the next cube number that continues the sequence.
Aptitude
Odd Man Out and Series
Difficulty: Easy
Choose an option
-
A354
-
B343
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C392
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D245
Answer
Correct Answer: 343
Explanation
Introduction / Context:This is a classic sequence of perfect cubes. Recognizing perfect powers (squares, cubes, fourth powers) is vital in numerical series questions.
Given Data / Assumptions:
- Terms given: 1, 8, 27, 64, 125, 216.
- These equal 1^3, 2^3, 3^3, 4^3, 5^3, 6^3 respectively.
Concept / Approach:Continue the natural-number base by one and compute the cube for the next term.
Step-by-Step Solution:
Identify last term's base: 216 = 6^3.Next base = 7.Compute 7^3 = 7 * 7 * 7 = 343.Verification / Alternative check:List of cubes: 1, 8, 27, 64, 125, 216, 343, 512, … The next clearly is 343.
Why Other Options Are Wrong:
- 354, 392, 245: None are perfect cubes; they do not match 7^3.
Common Pitfalls:Confusing cubes with squares or mixing arithmetic progressions into a powers sequence. Always test simple power patterns first.
Final Answer:343