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Find the missing number in the sequence: 4, 9, 19, 39, ?
79
89
59
69
79
Look at the differences or double the previous term and add a constant: (Term * 2) + 1.
Look at the differences or double the previous term and add a constant: (Term * 2) + 1.
Analyze consecutive differences
Find the difference between consecutive terms: 9 - 4 = 5, 19 - 9 = 10, 39 - 19 = 20. The differences are doubling each time (5, 10, 20).
Identify the next difference
Since the differences are 5, 10, 20, the next difference in the sequence must be 40.
Calculate the missing number
Add the next difference of 40 to the last given term: 39 + 40 = 79.
B: 89 is wrong because adding 50 instead of 40 gives 89. C: 59 is wrong because it uses an incorrect difference of 20 instead of 40. D: 69 is wrong because adding 30 is inconsistent with the doubling difference pattern.
A is correct because each term is obtained by multiplying the previous term by 2 and adding 1, or by adding a difference that doubles successively (4 + 5 = 9, 9 + 10 = 19, 19 + 20 = 39, 39 + 40 = 79).
In geometric or polynomial series, always check both the ratio between terms and the differences between consecutive terms to quickly spot exponential growth.
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