Determine the number that should replace the question mark (?) in the following sequence.

131, 143, 157, 175, 201, ?

The correct option is 243.

To find the missing number in the sequence, let's analyze the difference between consecutive terms:

First term: 131

Second term: 143

$143-131=12$

Third term: 157

$157-143=14$

Fourth term: 175

$175-157=18$

Fifth term: 201

$201-175=26$

Now, let's observe the sequence of first differences:

12, 14, 18, 26

Next, let's calculate the second differences (the differences between consecutive first differences):

$14-12=2$

$18-14=4$

$26-18=8$

The second differences are doubling at each step (2, 4, 8, ...), following powers of 2:

$2^1=2$

$2^2=4$

$2^3=8$

Following this pattern, the next second difference should be:

$2^4=16$

Adding 16 to the previous first difference (26) gives the next difference to add to 201:

$26+16=42$

Finally, add 42 to the last term (201) to find the missing number (?):

$201+42=243$

Thus, the number that replaces the question mark is 243.