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Find the next number in the series: 216, 125, 64, 27, ?
8
12
16
9
8
Recognize the sequence as a series of descending perfect cubes: n³ where n starts from 6 and decreases by 1.
Recognize the sequence as a series of descending perfect cubes: n³ where n starts from 6 and decreases by 1.
Analyze the series terms
Observe the numbers: 216 is 6 cubed (666), 125 is 5 cubed (555), 64 is 4 cubed (444), and 27 is 3 cubed (333).
Determine the pattern
The bases of the cubes follow a decreasing pattern: 6, 5, 4, 3. Therefore, the next number must be the cube of the next descending integer, which is 2.
Calculate the final result
Calculate 2 cubed: 2 * 2 * 2 = 8.
B: 12 is not a perfect cube; C: 16 is 4 squared but not part of the cube progression; D: 9 is 3 squared but not part of the cube progression.
A is correct because the series represents cubes of natural numbers in descending order (6³, 5³, 4³, 3³), leading to 2³ which equals 8.
For any number series involving large digits, quickly check if they are squares or cubes; memorizing cubes up to 10 saves significant time in RRB and Banking exams.
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