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Which of the following options should come in place of the question mark (?) in the given series? 5, 11, 23, 47, 95,?
189
191
193
195
191
Observe that each term is double the previous term plus one: (x * 2) + 1.
Observe that each term is double the previous term plus one: (x * 2) + 1.
Analyze the pattern
Calculate the difference or relationship between consecutive numbers: 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.
Apply the rule to the final term
To find the next term after 95, apply the same rule: (95 * 2) + 1. 95 * 2 = 190. 190 + 1 = 191.
A: 189 is incorrect because it is 190 - 1. C: 193 is incorrect because it represents (95 * 2) + 3. D: 195 is incorrect because it represents (95 * 2) + 5.
B is correct because the series follows the mathematical pattern of multiplying the previous term by 2 and adding 1, resulting in 191.
If the series grows rapidly, always check for multiplication patterns (x * 2, x * 3) or squared/cubed differences before looking for simple addition.