Question

The numbers \(x\), \(x+4\) and \(x+8\) are in A.P. with common difference:

• A. \(x\)
• B. \(4 + x\)
• C. 4
• D. 0

Hint:

Even if the terms contain a variable, the common difference is often a constant. Don't let the \(x\) confuse you; just follow the subtraction rule!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In an Arithmetic Progression (A.P.), the common difference (\(d\)) is the fixed value added to each term to get the next term.
Step 2: Key Formula or Approach:
\[ d = a_2 - a_1 = a_3 - a_2 \]
Step 3: Detailed Explanation:
1. Let the first term \(a_1 = x\).
2. Let the second term \(a_2 = x + 4\).
3. Calculate the difference:
\[ d = (x + 4) - x = 4 \] 4. Verify with the third term:
\[ d = (x + 8) - (x + 4) = x + 8 - x - 4 = 4 \] Since the difference is constant, \(d = 4\).
Step 4: Final Answer:
The common difference is 4.