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What should come in place of the question mark (?) in the given series? 2 16 44 100 212 ?
436
433
430
435
436
Observe the differences between consecutive terms; they follow a geometric progression of powers of 2 multiplied by 7, or simply doubling the previous difference plus a constant.
Observe the differences between consecutive terms; they follow a geometric progression of powers of 2 multiplied by 7, or simply doubling the previous difference plus a constant.
Analyze the difference between terms
Calculate consecutive differences: 16 - 2 = 14; 44 - 16 = 28; 100 - 44 = 56; 212 - 100 = 112.
Identify the pattern in differences
The differences are 14, 28, 56, 112. Each difference is double the previous one: 14 * 2 = 28, 28 * 2 = 56, 56 * 2 = 112.
Calculate the next term
The next difference must be 112 * 2 = 224. Adding this to the last term: 212 + 224 = 436.
B: 433 is incorrect as the next difference added to 212 results in 436, not 433. C: 430 is incorrect as it does not follow the doubling sequence of differences. D: 435 is incorrect as it fails to reach the mathematically derived sum of 436.
A is correct because the series follows an addition pattern where each term is the sum of the previous term and a doubling sequence of differences (14, 28, 56, 112, 224).
In any number series, if the terms grow rapidly, check for differences or product-based logic first; doubling the difference is a common pattern in competitive exams.
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