Directions: Identify the missing number that completes the pattern.

-31, -65, -133, -269, -541, ?, -2173, -4349

The correct option is -1085.

To identify the missing number that completes the pattern, let us analyze the relationship between consecutive terms in the series.

Let us examine the pattern step-by-step:

$\text{1st term to 2nd term:}(-31)\times 2-3=-62-3=-65$

$\text{2nd term to 3rd term:}(-65)\times 2-3=-130-3=-133$

$\text{3rd term to 4th term:}(-133)\times 2-3=-266-3=-269$

$\text{4th term to 5th term:}(-269)\times 2-3=-538-3=-541$

From the above calculations, we observe that each term is obtained by multiplying the previous term by 2 and then subtracting 3:

$\text{Next Term}=(\text{Current Term}\times 2)-3$

Applying this rule to find the missing 6th term (represented by '?'):

$\text{6th term}=(-541)\times 2-3=-1082-3=-1085$

Let us verify the remaining terms in the sequence using this calculated value (-1085):

$\text{7th term:}(-1085)\times 2-3=-2170-3=-2173$

$\text{8th term:}(-2173)\times 2-3=-4346-3=-4349$

The pattern holds true throughout the sequence. Thus, the missing number is -1085.