Question

If \( (2x - 1), 7, 3x \) are in A.P., then what is the value of \( x \)?

• A. 3
• B. 4
• C. 1
• D. 5

Hint:

In an A.P., the middle term is the average of the other two terms. Use this property to find unknown terms.

Answer 1

The Correct Option is B

In an A.P., the middle term is the average of the other two terms. Thus, we have: \[ 7 = \frac{(2x - 1) + 3x}{2}. \] Multiply both sides by 2: \[ 14 = (2x - 1) + 3x \quad \Rightarrow \quad 14 = 5x - 1. \] Solving for \( x \): \[ 14 + 1 = 5x \quad \Rightarrow \quad 15 = 5x \quad \Rightarrow \quad x = \frac{15}{5} = 3. \] Thus, the value of \( x \) is \( \boxed{4} \).