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What should come in place of the question mark (?) in the series: 100, 102, 106, 114, 130, ?
146
162
150
148
162
Observe the differences between consecutive terms; they are powers of 2 increasing sequentially (2, 4, 8, 16, 32).
Observe the differences between consecutive terms; they are powers of 2 increasing sequentially (2, 4, 8, 16, 32).
Analyze the difference between terms
Calculate the difference between consecutive terms: 102 - 100 = 2; 106 - 102 = 4; 114 - 106 = 8; 130 - 114 = 16.
Identify the pattern
The differences are 2, 4, 8, 16, which are powers of 2 (2¹, 2², 2³, 2⁴). Following this logic, the next difference must be 2⁵ = 32.
Calculate the missing number
Add the next difference to the last term: 130 + 32 = 162.
A: 146 is incorrect as it implies an addition of only 16; C: 150 is incorrect as it follows no logical progression; D: 148 is incorrect as it assumes a difference of 18 which breaks the power-of-2 pattern.
B is correct because the series follows a pattern of adding powers of 2 (2, 4, 8, 16, 32) to the previous term, resulting in 130 + 32 = 162.
Whenever numbers in a series are close to each other, always calculate the difference between terms first; if the differences form a secondary pattern, you have cracked the code.
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