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Find the missing number in the series: 4, 9, 19, 39,?
79
78
89
59
79
Observe that each term is generated by multiplying the previous term by 2 and adding 1 (n * 2 + 1).
Observe that each term is generated by multiplying the previous term by 2 and adding 1 (n * 2 + 1).
Analyze the pattern
Look at the differences between consecutive terms: 9-4=5, 19-9=10, 39-19=20. The differences are doubling (5, 10, 20).
Calculate the next term
Alternatively, use the formula (Term * 2) + 1. Applying this: 42+1=9; 92+1=19; 192+1=39. The next term is 392+1 = 78+1 = 79.
B: 78 is the result of only multiplying by 2 without adding the 1. C: 89 does not follow the doubling difference or the *2+1 pattern. D: 59 is obtained if one incorrectly adds only 20 instead of the next logical increment.
A is correct because the series follows the recursive pattern of multiplying the previous term by 2 and adding 1, resulting in 39 * 2 + 1 = 79.
When differences between numbers grow rapidly (like 5, 10, 20), always check for multiplication patterns or powers before assuming simple addition.