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Which of the following options should come in place of the question mark (?) in the given series? 7, 20, 59, 176,?, 1580
527
510
557
517
527
Calculate the difference or multiplier pattern: each term is (previous term * n) + addition, where n increases by 1 each step (starting at 2).
Calculate the difference or multiplier pattern: each term is (previous term * n) + addition, where n increases by 1 each step (starting at 2).
Analyze the series
The sequence is 7, 20, 59, 176, ?, 1580.
Determine the rule
Pattern: Term(n) = (Term(n-1) * 3) - 1. 73-1=20; 203-1=59; 59*3-1=176.
Calculate missing term
176 * 3 = 528. Then 528 - 1 = 527. Verification: 527 * 3 - 1 = 1581 - 1 = 1580, which matches the last term.
B: 510 is incorrect as it does not follow the x3-1 pattern. C: 557 is incorrect. D: 517 is incorrect.
A is correct because the series follows the mathematical pattern of multiplying the previous term by 3 and subtracting 1 (176 * 3 - 1 = 527).
In number series, if numbers grow very rapidly, always check multiplication patterns (x2, x3, etc.) first before checking additions of squares/cubes.
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