Instructions:

Identify the missing pair to complete the given numerical sequence:

(2, 1), (9, 2), (28, 3), (65, 4), ?, (217, 6)

The correct option is (126, 5).

To find the missing pair in the given sequence, let us analyze the relation between the numbers in each pair (x, y):

1^st pair: (2, 1)
Here, the second number is 1, and the first number is:
$1³+1=1+1=2$

2^nd pair: (9, 2)
Here, the second number is 2, and the first number is:
$2³+1=8+1=9$

3^rd pair: (28, 3)
Here, the second number is 3, and the first number is:
$3³+1=27+1=28$

4^th pair: (65, 4)
Here, the second number is 4, and the first number is:
$4³+1=64+1=65$

We can observe a clear pattern for the n-th pair (x, y):

$y=n$

$x=n^3+1$

Following this rule for the missing 5^th pair (where n = 5):

The second number is y = 5.

The first number is calculated as:

$x=5^3+1=125+1=126$

Thus, the missing pair is (126, 5).

We can double-check with the 6^th pair (217, 6):

For n = 6:
$y=6$
$x=6^3+1=216+1=217$

This confirms that the pattern holds true.

Therefore, the missing pair in the sequence is (126, 5).