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Find the missing number in the series: 4, 11, 30, 67, ?
128
130
125
121
128
Observe the proximity of each number to perfect cubes: (1┬│ + 3, 2┬│ + 3, 3┬│ + 3, 4┬│ + 3).
Observe the proximity of each number to perfect cubes: (1┬│ + 3, 2┬│ + 3, 3┬│ + 3, 4┬│ + 3).
Analyze the series terms
Given terms are 4, 11, 30, 67. We express each as n┬│ + 3: 1st term = 1 cubed + 3 = 1 + 3 = 4; 2nd term = 2 cubed + 3 = 8 + 3 = 11; 3rd term = 3 cubed + 3 = 27 + 3 = 30; 4th term = 4 cubed + 3 = 64 + 3 = 67.
Calculate the missing term
Following the pattern n┬│ + 3, the next term is the 5th term. Calculation: 5 cubed + 3 = 125 + 3 = 128.
B: 130 is incorrect because it is 128 plus 2, which does not fit the constant +3 pattern; C: 125 is just the cube of 5 and ignores the constant addition of 3; D: 121 is logically unrelated to the cubic growth pattern.
A is correct because the series follows the specific mathematical rule of adding 3 to the cube of the term position, resulting in 5 cubed plus 3, which equals 128.
Whenever numbers grow rapidly in a series, always check for squares (n┬▓) or cubes (n┬│) first before calculating the difference between terms.
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