If `4, x_(1), x_(2), x_(3), 28 `are in AP then `x_(3) = ?`

Options

A. 19
B. 23
C. 22
D. Cannot be determined

Explanation

To solve the problem where the numbers \(4, x_1, x_2, x_3, 28\) are in an Arithmetic Progression (AP), we need to find the value of \(x_3\).

### Step-by-Step Solution:

1. **Identify the first term and the fifth term**:
- The first term \(a = 4\).
- The fifth term \(a + 4d = 28\) (where \(d\) is the common difference).

2. **Set up the equation for the fifth term**:
- We can express the fifth term in terms of the first term and the common difference:
\[ 4 + 4d = 28 \]

3. **Solve for the common difference \(d\)**:
- Rearranging the equation gives:
\[ 4d = 28 - 4 \]
- Simplifying this:
\[ 4d = 24 \]
- Dividing both sides by 4:
\[ d = 6 \]

4. **Find \(x_3\)**:
- The term \(x_3\) is the fourth term in the sequence, which can be expressed as:
\[ x_3 = a + 3d \]
- Substituting the values of \(a\) and \(d\):
\[ x_3 = 4 + 3 \times 6 \]
- Calculating this gives:
\[ x_3 = 4 + 18 = 22 \]

5. **Conclusion**:
- Therefore, the value of \(x_3\) is \(22\).