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

To determine the common difference of the arithmetic progression (A.P.) consisting of the numbers \(x\), \(x+4\), and \(x+8\), we need to recall the property of an arithmetic progression where consecutive terms have a constant difference.

In an arithmetic progression, if \(a_1\), \(a_2\), \(a_3\), ..., are the terms, then the common difference \(d\) is given by:

\(d = a_2 - a_1 = a_3 - a_2\)

Now, apply this to the given numbers:

Here, \(a_1 = x\), \(a_2 = x + 4\), and \(a_3 = x + 8\).

Therefore, the common difference can be calculated as follows:

1. Calculate the difference between the second term and the first term:
2. Calculate the difference between the third term and the second term:

Both calculations yield the same common difference, which is 4. Therefore, the common difference \(d\) for the arithmetic progression is:

\(4\)

Thus, the correct answer is 4.