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What comes next in the series: 2, 5, 11, 23, 47,?
94
95
96
97
95
Observe that each number is approximately double the previous one; specifically, apply the rule (x * 2) + 1 to find the next term.
Observe that each number is approximately double the previous one; specifically, apply the rule (x * 2) + 1 to find the next term.
Analyze the pattern
Calculate the difference between consecutive terms: 5-2=3, 11-5=6, 23-11=12, 47-23=24. The differences are doubling (3, 6, 12, 24).
Apply the rule
Alternatively, use the formula (Term * 2) + 1: (22)+1=5, (52)+1=11, (112)+1=23, (232)+1=47.
Calculate the final term
Using the identified pattern: (47 * 2) + 1 = 94 + 1 = 95.
A: 94 ignores the addition of 1. C: 96 is a result of a miscalculation or incorrect pattern assumption. D: 97 follows a pattern of adding 3 instead of 1 in the final step, which contradicts the established sequence.
B is correct because the series follows the recursive formula of multiplying the previous term by 2 and adding 1, resulting in 47 * 2 + 1 = 95.
If the gap between numbers increases exponentially, always test for multiplication or powers; if the gap is small, test for addition or differences.