**Understanding the Problem:**

We are given that the sum of three terms in an arithmetic progression (AP) is 48. We need to find the middle term of the AP.

**Breaking Down the Problem:**

To solve this problem, we need to first understand the concept of an arithmetic progression and how it relates to finding the middle term.

1. **Arithmetic Progression (AP):** An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference (d).

2. **Sum of Three Terms in an AP:** The sum of three terms in an AP can be calculated using the formula:

S = (n/2) * (2a + (n-1)d)

where S is the sum of the terms, n is the number of terms, a is the first term, and d is the common difference.

3. **Finding the Middle Term:** In an AP with an odd number of terms, the middle term can be found by using the formula:

Middle Term = a + ((n-1)/2) * d

where a is the first term, n is the number of terms, and d is the common difference.

**Solution:**

Let's apply the above concepts to solve the problem step by step:

Step 1: Given that the sum of three terms in an AP is 48.

Step 2: We know that the sum of three terms in an AP can be calculated using the formula:

S = (n/2) * (2a + (n-1)d)

where S is the sum of the terms, n is the number of terms, a is the first term, and d is the common difference.

Plugging in the given values, we get:

48 = (3/2) * (2a + 2d)

Simplifying further, we have:

48 = (3/2) * (2a + 2d)

48 = (3/2) * (2(a + d))

48 = 3(a + d)

16 = a + d

Step 3: Since the given AP has three terms, it has an odd number of terms. Therefore, we can use the formula:

Middle Term = a + ((n-1)/2) * d

Plugging in the values, we have:

Middle Term = a + ((3-1)/2) * d

Middle Term = a + (2/2) * d

Middle Term = a + d

Substituting the value of a + d from Step 2, we get:

Middle Term = 16

Therefore, the middle term of the AP is 16.

**Conclusion:**

In an arithmetic progression where the sum of three terms is 48, the middle term is 16. We used the formula for the sum of three terms in an AP and the formula for finding the middle term in an AP with an odd number of terms to solve the problem.