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Find the missing number in the series: 12, 25, 51, 103, ?
205
207
209
211
207
Multiply each term by 2 and add 1 to get the next number in the sequence.
Multiply each term by 2 and add 1 to get the next number in the sequence.
Analyze the First Transition
Look at the relation between 12 and 25. Doubling 12 gives 24, and adding 1 gives 25 (12 * 2 + 1 = 25).
Verify the Pattern Across Terms
Check if the same rule applies to the next terms: 25 * 2 + 1 = 51, and 51 * 2 + 1 = 103. The pattern is consistently multiplied by 2 plus 1.
Calculate the Missing Number
Apply the rule to the last given term, 103: (103 * 2) + 1 = 206 + 1 = 207.
A: 205 is incorrect because it results from simple doubling without the +1 offset. C: 209 and D: 211 are incorrect as they deviate from the established multiplication and addition rule.
B is correct because applying the consistent rule of multiplying each term by 2 and adding 1 to 103 yields 207.
When numbers grow rapidly at an increasing rate, always check for combination series involving multiplication followed by an addition or subtraction.
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