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What should come in place of the question mark (?) in the given series? 146, 218, 340, 512, 734, ?
1128
1134
1006
1146
1006
Observe the differences between consecutive terms; they follow a clear sequence of multiples of 72.
Observe the differences between consecutive terms; they follow a clear sequence of multiples of 72.
Calculate the differences between consecutive terms
Find the difference between consecutive numbers: 218 - 146 = 72; 340 - 218 = 122; 512 - 340 = 172; 734 - 512 = 222.
Identify the pattern in the differences
The differences are 72, 122, 172, 222. Notice that the difference between these differences is a constant 50 (122 - 72 = 50, 172 - 122 = 50, 222 - 172 = 50).
Calculate the next term
The next difference must be 222 + 50 = 272. Adding this to the last term: 734 + 272 = 1006.
A: 1128 is incorrect as it results from adding 394, which does not follow the +50 difference pattern. B: 1134 is incorrect as it results from adding 400. D: 1146 is incorrect as it results from adding 412.
C is correct because the series follows a secondary difference of 50, leading to the next term being 734 + (222 + 50) = 1006.
If a series grows rapidly, always calculate the first and second levels of differences before assuming multiplication or power-based logic.
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