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 arithmetic mean of the terms on either side.

Answer 1

The Correct Option is A

For three numbers to be in A.P., the middle term is the average of the others:
\[ 7 - (2x - 1) = 3x - 7 \] Expanding: \[ 7 - 2x + 1 = 3x - 7 \] \[ 8 - 2x = 3x - 7 \] \[ 8 + 7 = 3x + 2x \] \[ 15 = 5x \Rightarrow x = 3. \]