Analyze the given number sequence to identify the underlying mathematical pattern and find the missing value.

756, 774, 738, 792, ?, 810

The correct answer is 720 (Option 3).

To find the missing number in the given sequence, let us analyze the pattern or differences between consecutive terms:

Given sequence: 756, 774, 738, 792, ?, 810

Let us look at the changes step-by-step:

1st step: From 756 to 774

$774-756=+18$

2nd step: From 774 to 738

$738-774=-36$

3rd step: From 738 to 792

$792-738=+54$

Notice the pattern in the differences:

$+18,-36,+54,...$

The differences are alternating in sign (plus, minus, plus, minus) and increase by multiples of 18 ($18\times 1$, $18\times 2$, $18\times 3$, $18\times 4$, $18\times 5$).

4th step: The next operation should be $-(18\times 4)=-72$.

Applying this to 792:

$792-72=720$

5th step: Let us verify the final term (810) using the next expected change, which is $+(18\times 5)=+90$:

$720+90=810$

This confirms our pattern. Therefore, the missing value is 720.