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What should come in place of the question mark (?) in the given series? 708 718 729 741 754 ?
767
765
766
768
768
Observe the differences between consecutive terms; the difference itself follows an increasing arithmetic sequence (+10, +11, +12, +13, +14).
Observe the differences between consecutive terms; the difference itself follows an increasing arithmetic sequence (+10, +11, +12, +13, +14).
Analyze consecutive differences
Calculate the difference between consecutive terms: 718 - 708 = 10, 729 - 718 = 11, 741 - 729 = 12, 754 - 741 = 13.
Identify the pattern and predict the next term
The differences are increasing by 1 (10, 11, 12, 13). Therefore, the next difference must be 14. Adding 14 to the last term: 754 + 14 = 768.
A: 767 is wrong as the increment would only be 13; B: 765 is wrong as the increment would be 11; C: 766 is wrong as the increment would be 12.
D is correct because the series follows an increasing gap pattern (+10, +11, +12, +13, +14), and 754 plus 14 equals 768.
When a series grows slowly, always check the differences between consecutive terms first; if the first layer of differences isn't constant, look at the second layer (the difference of the differences).
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