If 2, x, 26 are in A. P., then the value of x is.

Options

A. 28
B. 26
C. 14
D. 24

Answer

To find the value of \( x \) in the arithmetic progression (A.P.) where the terms are \( 2, x, 26 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding A.P.**: In an arithmetic progression, the middle term is the average of the other two terms. For three terms \( a, b, c \) in A.P., the relationship is given by:
\[ b = \frac{a + c}{2} \]
Here, \( a = 2 \), \( b = x \), and \( c = 26 \).

2. **Setting up the equation**: Substitute the values into the A.P. formula:
\[ x = \frac{2 + 26}{2} \]

3. **Calculating the sum**: First, calculate the sum of \( 2 \) and \( 26 \):
\[ 2 + 26 = 28 \]

4. **Finding the average**: Now divide the sum by \( 2 \):
\[ x = \frac{28}{2} = 14 \]

5. **Final answer**: Thus, the value of \( x \) is:
\[ x = 14 \]

### Summary:
The value of \( x \) is \( 14 \).