Find the number that should fill the position of the question mark (?) in the following sequence.

4, 262, 460, 606, 708, ?

The correct answer is 774.

To find the missing number in the sequence, let us analyze the differences between consecutive terms:
4, 262, 460, 606, 708, ?

Let us calculate the first-level differences (the difference between each term and the previous term):

$262-4=258$

$460-262=198$

$606-460=146$

$708-606=102$

Now, let us examine the sequence of these differences:
258, 198, 146, 102

Next, let us calculate the second-level differences (the difference between consecutive terms in the first-level differences sequence):

$258-198=60$

$198-146=52$

$146-102=44$

Notice that the second-level differences form a clear arithmetic progression: 60, 52, 44.
Each step decreases by 8:

$60-8=52$

$52-8=44$

Following this pattern, the next second-level difference should be:

$44-8=36$

Now, we use this value to find the next first-level difference:

$102-36=66$

Finally, we add this difference of 66 to the last term of the original sequence (708) to find the missing number (?):

$708+66=774$

Therefore, the number that fills the position of the question mark is 774.