`3, k-2,5` are in A.P, find` k.`

Answer

To find the value of \( k \) such that the numbers \( 3, k-2, 5 \) are in Arithmetic Progression (A.P.), we follow these steps:

### Step 1: Understand the condition for A.P.
In an A.P., the difference between consecutive terms is constant. This means:
\[ a_2 - a_1 = a_3 - a_2 \]
where \( a_1 = 3 \), \( a_2 = k - 2 \), and \( a_3 = 5 \).

### Step 2: Set up the equation
Using the condition for A.P., we can set up the equation:
\[ (k - 2) - 3 = 5 - (k - 2) \]

### Step 3: Simplify the equation
Now, simplify both sides:
\[ k - 2 - 3 = 5 - k + 2 \]
This simplifies to:
\[ k - 5 = 7 - k \]

### Step 4: Rearrange the equation
Next, rearranging the equation gives:
\[ k + k = 7 + 5 \]
or
\[ 2k = 12 \]

### Step 5: Solve for \( k \)
Now, divide both sides by 2:
\[ k = 6 \]

### Conclusion
Thus, the value of \( k \) is \( 6 \).