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What should come in place of the question mark (?) in the given series? 29 38 51 68 89 ?
115
116
114
113
114
Identify the difference between consecutive terms. The differences form a sequence of consecutive odd numbers starting from 9: 9, 13, 17, 21, 25.
Identify the difference between consecutive terms. The differences form a sequence of consecutive odd numbers starting from 9: 9, 13, 17, 21, 25.
Calculate consecutive differences
Find the difference between each term: 38-29=9, 51-38=13, 68-51=17, 89-68=21.
Identify the logic
The differences are 9, 13, 17, 21. These follow a pattern of adding 4 to the previous difference (9+4=13, 13+4=17, 17+4=21).
Find the next term
The next difference must be 21+4=25. Adding this to the last term: 89+25 = 114.
A: 115 is wrong as it results from a wrong difference of 26. B: 116 is wrong as it implies a different growth pattern. D: 113 is wrong as it is 89 + 24, which does not follow the +4 increment rule.
C is correct because the series follows an increasing gap pattern (9, 13, 17, 21, 25) added to consecutive terms starting from 29.
When the gaps between numbers are inconsistent, always check the 'second-order difference' (the difference of the differences) to reveal hidden arithmetic progressions.
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