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What should come in place of ‘?’ in the given series? 394, 465, 536, 607, 678, ?
768
736
756
749
749
Observe that the difference between consecutive terms is constant; calculate the difference between the first two terms and add it to the last term.
Observe that the difference between consecutive terms is constant; calculate the difference between the first two terms and add it to the last term.
Calculate the constant difference
Calculate the difference between consecutive terms: 465 - 394 = 71, 536 - 465 = 71, 607 - 536 = 71, 678 - 607 = 71. The common difference is 71.
Apply the difference to find the next term
Add 71 to the last given term (678) to find the missing value: 678 + 71 = 749.
A: 768 is incorrect because it is 678 + 90, failing the constant difference pattern; B: 736 is incorrect because it is 678 + 58; C: 756 is incorrect because it is 678 + 78.
D is correct because the series follows an arithmetic progression with a constant common difference of 71, and 678 plus 71 equals 749.
For any numerical series, always find the difference between the first two pairs. If they are identical, it is a simple additive series; if they vary, check for squares, cubes, or alternating patterns.
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