Answer :

To solve the problem of finding the missing number in the arithmetic sequence [tex]\(20, \ldots, 36, 44\)[/tex], we first need to determine if there is a common difference between the terms, which is characteristic of an arithmetic sequence.

Consider the given numbers: [tex]\(20\)[/tex], [tex]\(36\)[/tex], and [tex]\(44\)[/tex]. We need to find the common differences between consecutive terms:

1. Calculate the difference between the second term and the first term:
[tex]\[ 36 - 20 = 16 \][/tex]

2. Calculate the difference between the third term and the second term:
[tex]\[ 44 - 36 = 8 \][/tex]

For an arithmetic sequence, the common difference should be the same between all consecutive terms. Here, the differences are not the same (16 and 8).

To check if a number could potentially be missing, let's reasonably assume the sequence could be:
[tex]\[ 20, \ldots, 28, 36, 44 \][/tex]

Let's insert 28 as the potential missing number and check if it forms a valid arithmetic sequence:
3. Calculate the difference from 20 to 28:
[tex]\[ 28 - 20 = 8 \][/tex]

4. Calculate the difference from 28 to 36:
[tex]\[ 36 - 28 = 8 \][/tex]

Therefore, by inserting 28, we have the sequence:
[tex]\[ 20, 28, 36, 44 \][/tex]

The differences between consecutive terms are consistent (both are 8), which indeed forms an arithmetic sequence.

Thus, the missing number in the arithmetic sequence [tex]\(20, \ldots, 36, 44\)[/tex] is [tex]\(28\)[/tex].

Therefore, the correct answer is:
[tex]\[ \boxed{28} \][/tex]