Which of the following options will logically replace the question mark (?) to complete the given numerical series?

-12, -25, -52, -107, -218, ?

The correct option is -441.

To determine the missing number that logically replaces the question mark (?), let us analyze the step-by-step pattern between consecutive terms in the given numerical series:

-12, -25, -52, -107, -218, ?

Let us look at how each term is generated from the preceding term:

$1\text{st term to}2\text{nd term:}(-12)\times 2-1=-24-1=-25$

$2\text{nd term to}3\text{rd term:}(-25)\times 2-2=-50-2=-52$

$3\text{rd term to}4\text{th term:}(-52)\times 2-3=-104-3=-107$

$4\text{th term to}5\text{th term:}(-107)\times 2-4=-214-4=-218$

From the above steps, we can deduce the general rule for the pattern:
Each term is obtained by multiplying the previous term by 2 and then subtracting consecutive natural numbers (1, 2, 3, 4, 5, ...).

To find the 6^th term (?), we multiply the 5^th term (-218) by 2 and subtract 5:

$?=(-218)\times 2-5$

$?=-436-5=-441$

Therefore, the missing number in the series is -441.