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Select the missing number: 4, 9, 19, 39, ?
59
79
69
89
79
Multiply each term by 2 and add 1 (2x + 1 rule) to find the next term instantly.
Multiply each term by 2 and add 1 (2x + 1 rule) to find the next term instantly.
Analyze Differences
Find the difference between consecutive terms: 9 - 4 = 5, 19 - 9 = 10, and 39 - 19 = 20.
Identify Pattern
The differences double at each step (5, 10, 20). Therefore, the next difference must be 40.
Calculate Missing Term
Add the next difference (40) to the last term (39): 39 + 40 = 79.
A: 59 is incorrect because it assumes a stagnant or incorrect difference. C: 69 is incorrect as it fails to follow the doubling difference pattern. D: 89 is incorrect because it results from an overshot addition.
B is correct because the series follows the arithmetic rule where each term multiplied by 2 plus 1 gives the next term, and 39 x 2 + 1 = 79.
When terms grow rapidly, check for multiplying-plus-constant patterns before relying solely on simple difference trees.
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