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Which of the following options should come in place of the question mark (?) in the given series to make it logically complete? 10, 18, 38, 74, 150,?
274
298
300
280
298
Observe the pattern: Multiply by 2 and add increasing even numbers: 102-2=18, 182+2=38, 382-2=74, 742+2=150, 150*2-2=298.
Observe the pattern: Multiply by 2 and add increasing even numbers: 102-2=18, 182+2=38, 382-2=74, 742+2=150, 150*2-2=298.
Analyze the pattern
Looking at the differences between terms: 18-10=8, 38-18=20, 74-38=36, 150-74=76. Alternatively, observe the multiplicative logic: Term * 2 - 2 or + 2.
Verify sequence logic
10 * 2 = 20; 20 - 2 = 18. Then 18 * 2 = 36; 36 + 2 = 38. Then 38 * 2 = 76; 76 - 2 = 74. Then 74 * 2 = 148; 148 + 2 = 150.
Calculate the final term
Following the alternating sequence of operations (-2, +2, -2, +2), the next operation must be -2. 150 * 2 = 300; 300 - 2 = 298.
A: 274 is incorrect; C: 300 is incorrect; D: 280 is incorrect.
B is correct because the series follows a pattern of multiplying by 2 and then alternately subtracting 2 and adding 2, leading to 150 * 2 - 2 = 298.
In series with large jumps, always check for multiplication rules (e.g., x2, x3) combined with constant or alternating addition/subtraction.
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