If x, x+2, 3x are in A.P. then x = ?

Options

A. (a) 2
B. (b) 3
C. (c) 4
D. (d) 5

Answer

To find the value of \( x \) such that \( x, x + 2, 3x \) are in Arithmetic Progression (A.P.), we can follow these steps:

### Step 1: Understand the condition for A.P.
In an A.P., the difference between consecutive terms is constant. Therefore, we can set up the equation:
\[ \text{Second term} - \text{First term} = \text{Third term} - \text{Second term} \]

### Step 2: Identify the terms
Here, the first term is \( x \), the second term is \( x + 2 \), and the third term is \( 3x \).

### Step 3: Set up the equation
Using the A.P. condition:
\[ (x + 2) - x = 3x - (x + 2) \]

### Step 4: Simplify both sides
On the left side:
\[ x + 2 - x = 2 \]
On the right side:
\[ 3x - (x + 2) = 3x - x - 2 = 2x - 2 \]
So we have:
\[ 2 = 2x - 2 \]

### Step 5: Solve for \( x \)
Now, add 2 to both sides:
\[ 2 + 2 = 2x \]
This simplifies to:
\[ 4 = 2x \]
Now, divide both sides by 2:
\[ x = 2 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{2} \]

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