Choose the term that logically completes the following pattern of ordered pairs:

(4, 15), (5, 24), (6, 35), ?, (8, 63)

The correct option is (7, 48).

To find the missing term in the sequence of ordered pairs, let us analyze the pattern followed by both the first element and the second element of each pair $(x,y)$.

Step 1: Determine the first element (x)

The first elements of the given ordered pairs form the sequence:

$4,5,6,?,8$

Notice that each number increases by $1$. Therefore, the missing first element is:

$x=6+1=7$

Step 2: Determine the second element (y)

Now, let us examine how the second element $y$ relates to the first element $x$ in each pair:

For the pair $(4,15)$:

$y=4^2-1=16-1=15$

For the pair $(5,24)$:

$y=5^2-1=25-1=24$

For the pair $(6,35)$:

$y=6^2-1=36-1=35$

For the pair $(8,63)$:

$y=8^2-1=64-1=63$

The pattern for the second element is $y=x^2-1$.

Step 3: Calculate the missing term

Using $x=7$ in the rule $y=x^2-1$:

$y=7^2-1=49-1=48$

Therefore, the missing ordered pair is (7, 48).