Find the common difference of the Arithmetic Progression (A.P.)
`5, 14/3, 13/3, 4, .....`

Answer

To find the common difference of the Arithmetic Progression (A.P.) given by the terms \(5, \frac{14}{3}, \frac{13}{3}, 4, \ldots\), we will follow these steps:

### Step 1: Identify the terms of the A.P.
The first four terms of the A.P. are:
- \(T_1 = 5\)
- \(T_2 = \frac{14}{3}\)
- \(T_3 = \frac{13}{3}\)
- \(T_4 = 4\)

### Step 2: Calculate the common difference using the first two terms.
The common difference \(d\) can be calculated as:
\[ d = T_2 - T_1 \]
Substituting the values:
\[ d = \frac{14}{3} - 5 \]

### Step 3: Convert 5 to a fraction with a denominator of 3.
To perform the subtraction, we convert 5 into a fraction:
\[ 5 = \frac{15}{3} \]
Now substituting this back into the equation for \(d\):
\[ d = \frac{14}{3} - \frac{15}{3} \]

### Step 4: Perform the subtraction.
Now, we can subtract the fractions:
\[ d = \frac{14 - 15}{3} = \frac{-1}{3} \]

### Step 5: Conclusion.
Thus, the common difference \(d\) of the given A.P. is:
\[ d = -\frac{1}{3} \]