Question

If \((2x-1)\), \((3x+2)\) and \((6x-1)\) are three consecutive terms of an A.P., then the value of \(x\) is

• A. \(3\)
• B. \(2\)
• C. \(4\)
• D. \(1\)

Hint:

For three consecutive A.P. terms \(A,B,C\), the relation \(2B=A+C\) (or \(B=\frac{A+C}{2}\)) is the quickest route.

Answer 1

The Correct Option is A

Step 1: Use A.P. property.
In an A.P., the middle term equals the average of its neighbors:
\[ 3x+2=\frac{(2x-1)+(6x-1)}{2}=\frac{8x-2}{2}=4x-1. \]
Step 2: Solve for \(x\).
\[ 3x+2=4x-1 \ \Rightarrow\ x=3. \]