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What should come in place of the question mark (?) in the given series? 136 149 164 181 200 ?
295
285
221
247
221
Calculate the differences between consecutive terms; they follow a pattern of successive odd numbers (13, 15, 17, 19, 21).
Calculate the differences between consecutive terms; they follow a pattern of successive odd numbers (13, 15, 17, 19, 21).
Calculate differences between consecutive terms
149 - 136 = 13; 164 - 149 = 15; 181 - 164 = 17; 200 - 181 = 19.
Identify the pattern and predict the next term
The differences are consecutive odd numbers: 13, 15, 17, 19. The next odd number in the sequence is 21. Therefore, 200 + 21 = 221.
A: 295 is incorrect as it does not follow the +21 progression pattern; B: 285 is incorrect as it significantly exceeds the expected increment; D: 247 is incorrect because 200 + 47 does not maintain the established odd-number difference sequence.
C is correct because the series follows an increasing difference pattern of odd numbers (13, 15, 17, 19, 21), and adding 21 to 200 results in 221.
When the gaps between numbers are small and increasing, always check the difference of differences or the sequence of differences for a hidden arithmetic progression.
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