Question

The common difference of arithmetic progression 1, 5, 9, ... is

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

Finding the common difference is the most fundamental step in solving problems related to Arithmetic Progressions. Simply subtract any term from the term that follows it.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The common difference (\(d\)) of an Arithmetic Progression (A.P.) is the constant difference between any two consecutive terms.

Step 2: Key Formula or Approach:
\(d = a_2 - a_1\) or \(d = a_3 - a_2\), etc.

Step 3: Detailed Explanation:
The given A.P. is 1, 5, 9, ...
The first term (\(a_1\)) is 1.
The second term (\(a_2\)) is 5.
The third term (\(a_3\)) is 9.
Calculate the difference:
\[ d = a_2 - a_1 = 5 - 1 = 4 \] To be sure, let's check the next pair:
\[ d = a_3 - a_2 = 9 - 5 = 4 \] The difference is constant.

Step 4: Final Answer:
The common difference is 4.