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Find the missing number in the series: 5, 11, 23, 47, 95,?
189
191
193
195
191
Observe that each term is generated by doubling the previous number and adding one (n * 2 + 1).
Observe that each term is generated by doubling the previous number and adding one (n * 2 + 1).
Analyze the pattern
Calculate the difference or relationship between consecutive terms: 5 to 11 is (5 * 2) + 1 = 11; 11 to 23 is (11 * 2) + 1 = 23; 23 to 47 is (23 * 2) + 1 = 47; 47 to 95 is (47 * 2) + 1 = 95.
Calculate the missing term
Following the established pattern (n * 2 + 1), multiply the last term 95 by 2 and add 1: 95 * 2 = 190; 190 + 1 = 191.
A: 189 is incorrect as it results from 95 * 2 - 1. C: 193 is incorrect as it ignores the multiplier sequence. D: 195 is incorrect as it adds 5 instead of 1 to the doubled value.
B is correct because the series follows the constant logical rule of multiplying the previous term by 2 and adding 1, resulting in 95 * 2 + 1 = 191.
In number series, if the numbers increase rapidly, always test multiplication patterns combined with addition or subtraction before checking simple differences.