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What should come in place of '?' in the series: 5, 11, 23, 47, 95, ?
189
190
191
192
191
Observe that each term is generated by the formula: (Previous Term * 2) + 1. Quickly calculate 95 * 2 = 190 and add 1 to get 191.
Observe that each term is generated by the formula: (Previous Term * 2) + 1. Quickly calculate 95 * 2 = 190 and add 1 to get 191.
Analyze the pattern
Calculate the difference between consecutive terms: 11-5=6, 23-11=12, 47-23=24, 95-47=48. The differences are doubling (6, 12, 24, 48).
Identify the multiplier rule
Alternatively, identify the relationship: 52+1=11, 112+1=23, 232+1=47, 472+1=95.
Calculate the final term
Apply the rule to the last term: 95 * 2 + 1 = 190 + 1 = 191.
A: 189 is incorrect because it fails to follow the 2+1 pattern derived from the sequence. B: 190 is incorrect as it represents only the product (952) without the final increment of 1. D: 192 is incorrect as it is the result of 95*2+2, which does not fit the consistent +1 logic.
C is correct because the series follows the mathematical rule (Previous Term * 2) + 1, resulting in 95 * 2 + 1 = 191.
When terms in a number series increase rapidly (nearly doubling), always check for a multiplication-based pattern (e.g., n2+1, n2+2) before looking at simple differences.
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