Question

If \( K + 2, 4K - 6, 3K - 2 \) are three consecutive terms of an arithmetic progression, then the value of \( K \) is

• A. 4
• B. 3
• C. 2
• D. 1

Hint:

In an arithmetic progression, the difference between any two consecutive terms is always constant. Use this property to set up an equation and solve for unknowns.

Answer 1

The Correct Option is B

For the numbers to be in arithmetic progression, the difference between consecutive terms must be constant. Thus, the difference between the second and first terms should equal the difference between the third and second terms: \[ (4K - 6) - (K + 2) = (3K - 2) - (4K - 6). \] Simplifying both sides: \[ 3K - 8 = -K + 4. \] Solving for \( K \): \[ 3K + K = 4 + 8 \quad \Rightarrow \quad 4K = 12 \quad \Rightarrow \quad K = 3. \]