Which of the following numbers will replace the question mark (?) in the given series? 589, 588, 583, ?, 433, -192
558
Find the differences between consecutive terms: \(589 - 588 = 1\) and \(588 - 583 = 5\).
Check the last known difference: \(433 - (-192) = 625\). Since \(1 = 5^0\), \(5 = 5^1\) and \(625 = 5^4\), the differences follow powers of 5: 1, 5, 25, 125, 625.
So the missing term satisfies \(583 - x = 25\), giving \(x = 558\).
Verifying with the next difference: \(558 - 433 = 125\), which matches the expected pattern, confirming the missing number is 558.
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