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Find the missing number in the series: 1, 8, 27, 64, ?
72
81
100
125
125
Identify the numbers as perfect cubes of consecutive integers starting from 1 (1 cubed, 2 cubed, 3 cubed, 4 cubed, 5 cubed).
Identify the numbers as perfect cubes of consecutive integers starting from 1 (1 cubed, 2 cubed, 3 cubed, 4 cubed, 5 cubed).
Analyze the sequence
Observe the terms: 1 is 1 cubed (1 x 1 x 1), 8 is 2 cubed (2 x 2 x 2), 27 is 3 cubed (3 x 3 x 3), and 64 is 4 cubed (4 x 4 x 4).
Identify the rule
The series follows the pattern of n cubed where n is an incrementing integer starting from 1.
Calculate the missing term
The next term in the sequence is 5 cubed, which is 5 x 5 x 5 = 125.
A: 72 is not a perfect cube. B: 81 is 9 squared or 3 to the power of 4, not 5 cubed. C: 100 is 10 squared, not a perfect cube.
D is correct because the series follows a pattern of consecutive cubes (1┬│, 2┬│, 3┬│, 4┬│), making the next logical term 5┬│ = 125.
Always check for squares and cubes when a series grows rapidly; memorize cubes up to 15 and squares up to 30 to save significant time in exams.
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