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Which of the following options should come in place of the question mark (?) in the given series to make it logically complete? 125,128,133,140,149,?
156
160
158
154
160
Observe the differences between consecutive terms: 3, 5, 7, 9, 11... which are consecutive odd numbers! Add the next odd number (13) to the last term.
Observe the differences between consecutive terms: 3, 5, 7, 9, 11... which are consecutive odd numbers! Add the next odd number (13) to the last term.
Analyze consecutive differences
Find the difference between adjacent numbers in the series: 128 - 125 = 3, 133 - 128 = 5, 140 - 133 = 7, 149 - 140 = 9.
Identify the pattern rule
The differences form an arithmetic progression of consecutive odd numbers: 3, 5, 7, 9. The next odd number in sequence is 11.
Calculate the missing term
Add the next difference (11) to the last given term: 149 + 11 = 160.
A: 156 is incorrect because adding 7 instead of 11 leads to an incorrect step; C: 158 is incorrect as it corresponds to adding 9 twice incorrectly; D: 154 is incorrect because it subtracts or applies a wrong increment.
B is correct because the series increases by consecutive odd numbers (3, 5, 7, 9, 11), giving 149 + 11 = 160.
Always check both single differences and double differences (difference of differences) when the first-order differences form an arithmetic progression.
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